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A347142
Sum of 4th powers of divisors of n that are < sqrt(n).
4
0, 1, 1, 1, 1, 17, 1, 17, 1, 17, 1, 98, 1, 17, 82, 17, 1, 98, 1, 273, 82, 17, 1, 354, 1, 17, 82, 273, 1, 723, 1, 273, 82, 17, 626, 354, 1, 17, 82, 898, 1, 1394, 1, 273, 707, 17, 1, 1650, 1, 642, 82, 273, 1, 1394, 626, 2674, 82, 17, 1, 2275, 1, 17, 2483, 273, 626
OFFSET
1,6
FORMULA
G.f.: Sum_{k>=1} k^4 * x^(k*(k + 1)) / (1 - x^k).
MATHEMATICA
Table[DivisorSum[n, #^4 &, # < Sqrt[n] &], {n, 1, 65}]
nmax = 65; CoefficientList[Series[Sum[k^4 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) A347142(n) = { my(s=0); fordiv(n, d, if((d^2)>=n, return(s)); s += (d^4)); }; \\ Antti Karttunen, Aug 19 2021
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 19 2021
STATUS
approved