A370250 Numbers k such that the sum of the digits times the square of the sum of the fourth powers of the digits equals k.

0, 1, 5873656512, 7253758561, 29961747275

Offset: 1

Author

René-Louis Clerc, Feb 13 2024

Keywords

• nonn
• base
• fini
• full

Comments

There are exactly 5 such numbers (Property 17 of Clerc).

Examples

			7253758561 = (7+2+5+3+7+5+8+5+6+1)*(7^4 + 2^4 + 5^4 + 3^4 + 7^4 + 5^4 + 8^4 + 5^4 + 6^4 + 1^4)^2 = 49*148035889 = 7253758561.
		

Links

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

Crossrefs

Cf. A368939, A115518, A257766, A061209, A061210, A254000, A130680, A366507, A366512.

Programs

PARI

niven142(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^4)^2 == k;
for(k=0,10^12,if(niven142(k)==1,print1(k, ", ")))