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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.
0
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
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
Sequence in context: A133505 A068407 A334601 * A116960 A126957 A228187
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006
EXTENSIONS
Corrected by Michel Marcus, Feb 27 2014
STATUS
approved