A number n such that σ(n) < 2n more
The first 600 deficient numbers :
1,
2,
3,
4,
5,
7,
8,
9,
10,
11,
13,
14,
15,
16,
17,
19,
21,
22,
23,
25,
26,
27,
29,
31,
32,
33,
34,
35,
37,
38,
39,
41,
43,
44,
45,
46,
47,
49,
50,
51,
52,
53,
55,
57,
58,
59,
61,
62,
63,
64,
65,
67,
68,
69,
71,
73,
74,
75,
76,
77,
79,
81,
82,
83,
85,
86,
87,
89,
91,
92,
93,
94,
95,
97,
98,
99,
101,
103,
105,
106,
107,
109,
110,
111,
113,
115,
116,
117,
118,
119,
121,
122,
123,
124,
125,
127,
128,
129,
130,
131,
133,
134,
135,
136,
137,
139,
141,
142,
143,
145,
146,
147,
148,
149,
151,
152,
153,
154,
155,
157,
158,
159,
161,
163,
164,
165,
166,
167,
169,
170,
171,
172,
173,
175,
177,
178,
179,
181,
182,
183,
184,
185,
187,
188,
189,
190,
191,
193,
194,
195,
197,
199,
201,
202,
203,
205,
206,
207,
209,
211,
212,
213,
214,
215,
217,
218,
219,
221,
223,
225,
226,
227,
229,
230,
231,
232,
233,
235,
236,
237,
238,
239,
241,
242,
243,
244,
245,
247,
248,
249,
250,
251,
253,
254,
255,
256,
257,
259,
261,
262,
263,
265,
266,
267,
268,
269,
271,
273,
274,
275,
277,
278,
279,
281,
283,
284,
285,
286,
287,
289,
290,
291,
292,
293,
295,
296,
297,
298,
299,
301,
302,
303,
305,
307,
309,
310,
311,
313,
314,
315,
316,
317,
319,
321,
322,
323,
325,
326,
327,
328,
329,
331,
332,
333,
334,
335,
337,
338,
339,
341,
343,
344,
345,
346,
347,
349,
351,
353,
355,
356,
357,
358,
359,
361,
362,
363,
365,
367,
369,
370,
371,
373,
374,
375,
376,
377,
379,
381,
382,
383,
385,
386,
387,
388,
389,
391,
393,
394,
395,
397,
398,
399,
401,
403,
404,
405,
406,
407,
409,
410,
411,
412,
413,
415,
417,
418,
419,
421,
422,
423,
424,
425,
427,
428,
429,
430,
431,
433,
434,
435,
436,
437,
439,
441,
442,
443,
445,
446,
447,
449,
451,
452,
453,
454,
455,
457,
458,
459,
461,
463,
465,
466,
467,
469,
470,
471,
472,
473,
475,
477,
478,
479,
481,
482,
483,
484,
485,
487,
488,
489,
491,
493,
494,
495,
497,
499,
501,
502,
503,
505,
506,
507,
508,
509,
511,
512,
513,
514,
515,
517,
518,
519,
521,
523,
524,
525,
526,
527,
529,
530,
531,
533,
535,
536,
537,
538,
539,
541,
542,
543,
545,
547,
548,
549,
551,
553,
554,
555,
556,
557,
559,
561,
562,
563,
565,
566,
567,
568,
569,
571,
573,
574,
575,
577,
578,
579,
581,
583,
584,
585,
586,
587,
589,
590,
591,
592,
593,
595,
596,
597,
598,
599,
601,
602,
603,
604,
605,
607,
609,
610,
611,
613,
614,
615,
617,
619,
621,
622,
623,
625,
626,
627,
628,
629,
631,
632,
633,
634,
635,
637,
638,
639,
641,
643,
645,
646,
647,
649,
651,
652,
653,
655,
656,
657,
658,
659,
661,
662,
663,
664,
665,
667,
668,
669,
670,
671,
673,
674,
675,
676,
677,
679,
681,
682,
683,
685,
686,
687,
688,
689,
691,
692,
693,
694,
695,
697,
698,
699,
701,
703,
705,
706,
707,
709,
710,
711,
712,
713,
715,
716,
717,
718,
719,
721,
722,
723,
724,
725,
727,
729,
730,
731,
733,
734,
735,
737,
739,
741,
742,
743,
745,
746,
747,
749,
751,
752,
753,
754,
755,
757,
758,
759,
761,
763,
764,
765,
766,
767,
769,
771,
772,
773,
775,
776,
777,
778,
779,
781,
782,
783,
785,
787,
788,
789,
790,
791,
793,
794,
795,
796.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 7523259 values, from 1 to 9999999).
n\r | 0 | 1 |
2 | 2543920 | 4979339 | 2 |
3 | 1646006 | 2938632 | 2938621 | 3 |
4 | 950545 | 2489674 | 1593375 | 2489665 | 4 |
5 | 1242298 | 1570256 | 1570228 | 1570232 | 1570245 | 5 |
6 | 0 | 1666667 | 1271955 | 1646006 | 1271965 | 1666666 | 6 |
7 | 885249 | 1106312 | 1106333 | 1106334 | 1106339 | 1106335 | 1106357 | 7 |
8 | 392791 | 1244843 | 796695 | 1244830 | 557754 | 1244831 | 796680 | 1244835 | 8 |
9 | 539185 | 979531 | 979545 | 553412 | 979533 | 979540 | 553409 | 979568 | 979536 | 9 |
10 | 262669 | 999928 | 570297 | 999924 | 570318 | 979629 | 570328 | 999931 | 570308 | 999927 | 10 |
11 | 621829 | 690124 | 690171 | 690142 | 690168 | 690125 | 690154 | 690133 | 690150 | 690137 | 690126 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.