A364601 Numbers m such that, if k is the number of digits of m, then for some r > 1, the sum of the k-th powers of the digits of m^r is equal to m.

1, 7, 8, 9, 180, 205, 38998, 45994, 89080, 726191, 5540343, 7491889, 8690141, 167535050, 749387107, 9945245922

Offset

1,2

Comments

Corresponding r's: any, 4, 3, 2, 6, 2, 2, 2, 2, 2, 3, 2, 3, 3, 4, 3.

Links

Table of n, a(n) for n=1..16.

René-Louis Clerc, Pleasant transformations and a new class of narcissistic perfect numbers, hal-03619147, 2022-2023.

René-Louis Clerc, The Perfect R-Narcissistic Numbers, 2023.

René-Louis Clerc, Perfect r-narcissistic numbers in any base, hal-04376934, 2024.

René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)

Example

180 with r=6 satisfies: 180^6 = 34012224000000, 3^3 + 4^3 + 1 + 2^3 + 2^3 + 2^3 + 4^3 = 180.

Prog

(PARI) SomP(n, p)={resu=0; for(i=1, #digits(n), resu+=(digits(n)[i])^p); resu}
Ppdi(k, r)={for(n=10^(k-1), 10^k, if(SomP(n^r, k)==n, print1(n, "; ")))}

Crossrefs

Cf. A005188 (Armstrong's numbers, case r=1 in our terminology).

Cf. A066003, A066004, A065999 (for terms 7, 8 and 9).

Sequence in context: A048009 A048046 A048092 * A337468 A105860 A096677

Adjacent sequences: A364598 A364599 A364600 * A364602 A364603 A364604

Keyword

nonn,base,fini,more

Author

René-Louis Clerc, Jul 29 2023

Status

approved