A117732 Numbers k that divide s(k)^w(k), where s(k) is the sum of the digits of k and w(k) is the digital root of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 27, 48, 81, 192, 243, 288, 375, 392, 486, 512, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2187, 2401, 2592, 2916, 3456, 4374, 4608, 4802, 4913, 5184, 5832, 6561, 6912, 10368, 11664, 13824, 15552, 17576, 19683, 20736, 23328

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

392 is in the sequence because (1) s(392) = 3 + 9 + 2 = 14 and w(392) = 1 + 4 = 5, and (2) 14^5 = 537824 is divisible by 392.

Mathematica

Select[Range[10^5], Divisible[Total@IntegerDigits@#^FixedPoint[Total@IntegerDigits@#&, #], #]&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

Prog

(PARI) a010888(n) = (n-1)%9+1;
isok(n) = !(sumdigits(n)^a010888(n) % n); \\ Michel Marcus, Feb 27 2014

Crossrefs

Cf. A007953, A010888.

Sequence in context: A133505 A068407 A334601 * A116960 A126957 A228187

Adjacent sequences: A117729 A117730 A117731 * A117733 A117734 A117735

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006

Extensions

Corrected by Michel Marcus, Feb 27 2014

Status

approved