A368939 Numbers k such that the sum of the digits times the sum of the fourth powers of the digits equals k.

0, 1, 182380, 444992

Offset

1,3

Comments

There are exactly 4 such numbers (Property 16 of Clerc).

Links

Table of n, a(n) for n=1..4.

René-Louis Clerc, Quelques nombres de Niven-Harshad particuliers, 2023.

Example

182380 = (1+8+2+3+8)*(1^4 + 8^4 + 2^4 + 3^4 + 8^4) = 22*8290.

Mathematica

Select[Range[0, 10^7], #==Total[IntegerDigits[#]]*Total[IntegerDigits[#]^4]&] (* James C. McMahon, Jan 11 2024 *)

Prog

(PARI) niven14(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^4) == k;
for(k=1, 10^7, if(niven14(k)==1, print1(k, ", ")))

Crossrefs

Cf. A115518, A257766, A061209, A061210, A254000, A130680, A366507, A366512.

Sequence in context: A249959 A250013 A258842 * A030466 A233956 A249232

Adjacent sequences: A368936 A368937 A368938 * A368940 A368941 A368942

Keyword

nonn,base,fini,full,bref

Author

René-Louis Clerc, Jan 10 2024

Status

approved