A007603 Power-sum numbers: let n = a_1 a_2 ... a_k be a k-digit number; n is a power-sum number if there are exponents e_1 ... e_m such that n = Sum_{i=1..m} Sum_{j=1..k} a_j^e_i. (Formerly M0480)

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 23, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 104, 108, 110, 111, 112, 113, 114, 115, 116, 117, 120, 122, 126, 130, 131, 132, 133, 134, 135, 136, 140, 144, 150, 151, 152, 153, 154, 156, 160, 162, 170, 171, 172, 173, 174, 178, 180, 182

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mike Keith, Power-sum numbers, J. Recreational Mathematics, Vol. 18, No. 4 (1986), pp. 275-278. (Annotated scanned copy)

Example

21 = (2+1)+(2^3+1^3)+(2^3+1^3), with e_1, e_2, e_3 = 1, 3, 3.

Mathematica

q[n_] := Module[{d = IntegerDigits[n], v = {}, k = 1, s, ans = False}, If[Max[d] == 1, ans = Divisible[n, Total[d]], While[(s = Total[d^k]) <= n, AppendTo[v, s]; If[Length[IntegerPartitions[n, All, v]] > 0, ans = True; Break[]]; k++]]; ans]; Select[Range[200], q] (* Amiram Eldar, Sep 04 2021 *)

Crossrefs

Subsequences: A005349, A034087, A034088, A169665, A169666.

Sequence in context: A143289 A064807 A235591 * A005349 A234474 A285829

Adjacent sequences: A007600 A007601 A007602 * A007604 A007605 A007606

Keyword

nonn,easy,nice,base

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Extensions

Corrected and extended by Naohiro Nomoto, Mar 11 2001

Status

approved