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centered nonagonal numbers
Centered nonagonal numbers are figurate numbers (see picture aside) defined as  $N_n=9n(n-1)/2+1$. All the centered nonagonal numbers are triangular numbers too.

Three formulas involving centered nonagonal numbers:

\[\sum_{n=1}^{\infty}\frac{1}{N_n}=\frac{2 \pi }{3 \sqrt{3}}\,,\quad \sum_{n=0}^{\infty}\frac{N_n}{n!}=\frac{11}{2}e\,, \quad\mbox{and}\quad\sum_{n=1}^{\infty}\frac{N_n}{2^n}=19\,. \]

The first centered nonagonal numbers are 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of centered nonagonal numbers

A graph displaying how many centered nonagonal numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of centered nonagonal numbers
Useful links Wikipedia, Centered nonagonal number
OEIS, Sequence A060544
Centered nonagonal numbers can also be... (you may click on names or numbers and on + to get more values)

aban 10 28 55 + 999949000753 abundant 820 1540 2080 + 49765276 admirable 491536 alternating 10 325 496 + 969694741 amenable 28 136 253 + 999916840 apocalyptic 820 1081 1891 + 29890 arithmetic 55 91 190 + 9997156 binomial 10 28 55 + 9999993493045 brilliant 10 253 703 + 998977951 c.decagonal 1711 2467531 3558178261 5130890585101 c.heptagonal 253 64261 16322041 + 267457893082381 c.octagonal 1225 1413721 1631432881 1882672131025 c.pentagonal 1891 88831 196049701 + 954928097357851 c.triangular 10 136 1891 + 519499406175760 canyon 325 406 703 + 987612346 Carmichael 8911 10585 41041 + 921323712961 congruent 28 55 136 + 9970345 constructible 10 136 32896 2147516416 Cunningham 10 28 325 + 575598885856165 cyclic 91 595 703 + 9916831 d-powerful 16471 24976 32896 + 7882435 de Polignac 79003 93961 166753 + 99934453 decagonal 10 1540 11935 + 18342198104230 deceptive 91 703 8911 + 99851537521 deficient 10 55 91 + 9983746 dig.balanced 10 595 820 + 199690120 Duffinian 55 253 325 + 9956953 eban 36046 40002040 32064036004000 economical 10 1081 1225 + 19911205 emirpimes 1891 3403 5671 + 97531561 equidigital 10 1081 1225 + 19911205 esthetic 10 evil 10 136 190 + 999916840 fibodiv 28 Fibonacci 55 Friedman 293761 419986 597871 857395 frugal 130816 195625 1413721 + 957053125 gapful 190 253 1540 + 99969549085 happy 10 28 91 + 9956953 harmonic 28 496 8128 + 137438691328 Harshad 10 190 820 + 9999171820 heptagonal 55 121771 5720653 + 593128762435 hex 91 8911 873181 + 80505887094361 hexagonal 28 91 190 + 999999818878690 hoax 136 11476 12880 + 99003556 Hogben 91 703 104653 + 160829915470003 hyperperfect 28 325 496 + 137438691328 iban 10 703 1711 + 442270 idoneal 10 28 190 253 interprime 7381 87571 88831 + 99426151 junction 406 820 3916 + 99892045 Kaprekar 55 703 5050 + 50000005000000 katadrome 10 91 820 + 86320 Lehmer 91 595 703 + 999406030321 lucky 1711 3403 3655 + 9916831 magnanimous 136 6824665 metadrome 28 136 1378 modest 406 7021 140185 + 1984027528 Moran 190 mountain 190 253 496 + 1269853210 nialpdrome 10 55 91 + 87777776521 nonagonal 325 82621 20985481 + 343874433963061 nude 55 8128 881128 + 127241128 oban 10 28 55 + 820 octagonal 1957283461 1086210502741 odious 28 55 91 + 999782686 palindromic 55 595 5995 + 683727232727386 panconsummate 10 91 pandigital 2926 23005 29890 + 339861556 pentagonal 7906276 57722156241751 perfect 28 496 8128 + 137438691328 pernicious 10 28 55 + 9890128 Perrin 10 persistent 11930258746 12874106953 16209451378 + 76895321041 plaindrome 28 55 136 + 22222227777778 Poulet 2701 8911 10585 + 999961448323753 power 1225 1413721 1631432881 1882672131025 powerful 1225 1413721 1631432881 1882672131025 practical 28 496 820 + 9823528 prim.abundant 30628 491536 575128 + 55551070 productive 28 136 pseudoperfect 28 496 820 + 33550336 repdigit 55 repfigit 28 repunit 91 703 820 + 231627523606480 Ruth-Aaron 4186 247456 540280 + 803842895485 self 703 3403 4753 + 999246160 semiprime 10 55 91 + 99214741 Smith 29890 32896 141778 + 99680140 sphenic 190 406 595 + 99934453 square 1225 1413721 1631432881 1882672131025 star 253 49141 9533161 + 69599723176621 super Niven 10 2080 5050 + 5000050000 super-d 190 1081 2926 + 9916831 tau 136 12880 32896 + 999246160 taxicab 61249825000 tetrahedral 10 1540 triangular 10 28 55 + 999999953042761 uban 10 28 55 + 98000077000015 Ulam 28 253 820 + 9956953 undulating 595 5050 unprimeable 325 2485 4186 + 9997156 untouchable 406 7750 12880 + 958420 upside-down 28 55 91 wasteful 28 55 91 + 9997156 Zumkeller 28 496 820 + 96580 zygodrome 55 111221155