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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
0, 1, 5873656512, 7253758561, 29961747275
OFFSET
1,3
COMMENTS
There are exactly 5 such numbers (Property 17 of Clerc).
EXAMPLE
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.
PROG
(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, ", ")))
KEYWORD
nonn,base,fini,full
AUTHOR
René-Louis Clerc, Feb 13 2024
STATUS
approved