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

Author

René-Louis Clerc, Jan 10 2024

Keywords

• nonn
• base
• fini
• full
• bref

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

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,", ")))