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insolite numbers
A number    is said to be insolite if it is divisible by the sum and by the product of the squares of its digits.

For example, 122121216 is insolite since it is divisible by

and by

There are only 428 insolite numbers below  .

Only few insolite numbers are known to include the digit '5'. Indeed, the zerolessness conditions prescribe that in this case the number is made of an odd number of odd digits.

The table below reports the smallest insolite numbers containing a specific digit.

dn
2 11112, 1122112, 122121216, 1111112112
3 1111211136, 11111113116, 11132111232
4 11121114112, 121121114112, 211121114112
5 1111111111131111131111111111175
6 122121216, 1111211136, 1116122112
7 123412112474112, 211912113131712
8 121111216128, 911131213824
9 911131213824, 211912113131712

The second smallest insolite number cointaining the digit 5 could by

while the smallest insolite number containing all the digits except 5 is 711813411914121216.

Every number greater than 2644145 can be written as the sum of insolite numbers.

The first insolite numbers are 111, 11112, 1122112, 111111111, 122121216, 1111112112, 1111211136, 1116122112, 1211162112, 11111113116 more terms

Insolite numbers can also be... (you may click on names or numbers and on + to get more values)