A368939 - OEIS

%I #18 Feb 06 2024 11:55:15

%S 0,1,182380,444992

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

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

%H René-Louis Clerc, <a href="https://hal.science/hal-04235744">Quelques nombres de Niven-Harshad particuliers</a>, 2023.

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

%t Select[Range[0,10^7],#==Total[IntegerDigits[#]]*Total[IntegerDigits[#]^4]&] (* _James C. McMahon_, Jan 11 2024 *)

%o (PARI) niven14(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^4) == k;

%o for(k=1,10^7,if(niven14(k)==1,print1(k,", ")))

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

%K nonn,base,fini,full,bref

%O 1,3

%A _René-Louis Clerc_, Jan 10 2024