VOOZH about

URL: https://oeis.org/A347173

⇱ A347173 - OEIS

login
A347173
Sum of squares of odd divisors of n that are <= sqrt(n).
3
1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 26, 1, 10, 1, 1, 35, 1, 1, 10, 1, 26, 10, 1, 1, 10, 26, 1, 10, 1, 1, 35, 1, 1, 10, 50, 26, 10, 1, 1, 10, 26, 50, 10, 1, 1, 35, 1, 1, 59, 1, 26, 10, 1, 1, 10, 75, 1, 10, 1, 1, 35, 1, 50, 10, 1, 26
OFFSET
1,9
LINKS
FORMULA
G.f.: Sum_{k>=1} (2*k - 1)^2 * x^((2*k - 1)^2) / (1 - x^(2*k - 1)).
EXAMPLE
a(18) = 10 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 squares of 1 and 3 then add them i.e., a(18) = 1^2 + 3^2 = 10. - David A. Corneth, Feb 24 2024
MATHEMATICA
Table[DivisorSum[n, #^2 &, # <= Sqrt[n] && OddQ[#] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[(2 k - 1)^2 x^((2 k - 1)^2)/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sum(k=0, sqrtint(n), if ((k%2) && !(n%k), k^2)); \\ Michel Marcus, Aug 22 2021
(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]^2
,
return(res)
)
); res
} \\ David A. Corneth, Feb 24 2024
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Aug 21 2021
STATUS
approved