A241754 Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n, for some d with 1 <= d < length(n).
132, 264, 396, 35964, 4799520, 839991600, 1511984880, 332639667360, 86486391351360, 151351184864880, 46126079538739200, 27427196132572803840, 18050376958194962304000, 7828706350001712936499200, 8540406927274595930726400
Offset: 1
Examples
sum(132,2) = 13 + 31 + 32 + 23 + 12 + 21 = 132.
Links
- Anthony Sand, Table of n, a(n) for n = 1..22
Formula
For a number n with d1 digits there are d1Pd2 = d1!/(d1-d2)! substrings generated by sampling and permutating d2 digits from the original number. When n=132 and d2=2, these substrings are 13, 31, 32, 23, 12, 21. When n=112 and d2=2, the substrings are 11, 11, 12, 21, 12, 21. Sum(x,d) is defined as the sum of d-digit substrings for a number x. The sequence above is those numbers such that sum(x,d) = x, where d = 2, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 11, 12, 12, 13, 13, 14, 14.