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URL: https://oeis.org/A347175

⇱ A347175 - OEIS

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A347175
Sum of 4th powers of odd divisors of n that are <= sqrt(n).
3
1, 1, 1, 1, 1, 1, 1, 1, 82, 1, 1, 82, 1, 1, 82, 1, 1, 82, 1, 1, 82, 1, 1, 82, 626, 1, 82, 1, 1, 707, 1, 1, 82, 1, 626, 82, 1, 1, 82, 626, 1, 82, 1, 1, 707, 1, 1, 82, 2402, 626, 82, 1, 1, 82, 626, 2402, 82, 1, 1, 707, 1, 1, 2483, 1, 626, 82, 1, 1, 82, 3027, 1, 82, 1, 1, 707
OFFSET
1,9
LINKS
FORMULA
G.f.: Sum_{k>=1} (2*k - 1)^4 * x^((2*k - 1)^2) / (1 - x^(2*k - 1)).
EXAMPLE
a(18) = 82 as the odd divisors of 18 are the divisors of 9 which are 1, 3 and 9. Of those, 1 and 3 are <= sqrt(18) so we find the sum of fourth powers of 1 and 3 then add them i.e., a(18) = 1^4 + 3^4 = 82. - David A. Corneth, Feb 24 2024
MATHEMATICA
Table[DivisorSum[n, #^4 &, # <= Sqrt[n] && OddQ[#] &], {n, 1, 75}]
nmax = 75; CoefficientList[Series[Sum[(2 k - 1)^4 x^((2 k - 1)^2)/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI)
a(n) = {
my(s = sqrtint(n), res);
n>>=valuation(n, 2);
d = divisors(n);
for(i = 1, #d,
if(d[i] <= s,
res += d[i]^4
,
return(res)
)
); res
} \\ David A. Corneth, Feb 24 2024
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Aug 21 2021
STATUS
approved