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 A352048 Sum of the squares of the divisor complements of the odd proper divisors of n. 11
 0, 4, 9, 16, 25, 40, 49, 64, 90, 104, 121, 160, 169, 200, 259, 256, 289, 364, 361, 416, 499, 488, 529, 640, 650, 680, 819, 800, 841, 1040, 961, 1024, 1219, 1160, 1299, 1456, 1369, 1448, 1699, 1664, 1681, 2000, 1849, 1952, 2365, 2120, 2209, 2560, 2450, 2604, 2899, 2720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n^2 * Sum_{d|n, d=2} k^2 * x^k / (1 - x^(2*k)). - Ilya Gutkovskiy, May 14 2023 From Amiram Eldar, Oct 13 2023: (Start) a(n) = A050999(n) * A006519(n)^2 - A000035(n). Sum_{k=1..n} a(k) = c * n^3 / 3, where c = 7*zeta(3))/8 = 1.0517997... (A233091). (End) EXAMPLE a(10) = 10^2 * Sum_{d|10, d<10, d odd} 1 / d^2 = 10^2 * (1/1^2 + 1/5^2) = 104. MAPLE f:= proc(n) local m, d; m:= n/2^padic:-ordp(n, 2); add((n/d)^2, d = select(`<`, numtheory:-divisors(m), n)) end proc: map(f, [\$1..60]); # Robert Israel, Apr 03 2023 MATHEMATICA a[n_] := n^2 DivisorSum[n, If[# < n && OddQ[#], 1/#^2, 0]&]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 11 2023 *) a[n_] := DivisorSigma[-2, n/2^IntegerExponent[n, 2]] * n^2 - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *) PROG (PARI) a(n) = n^2*sumdiv(n, d, if ((d> valuation(n, 2), -2) - n % 2; \\ Amiram Eldar, Oct 13 2023 CROSSREFS Sum of the k-th powers of the divisor complements of the odd proper divisors of n for k=0..10: A091954 (k=0), A352047 (k=1), this sequence (k=2), A352049 (k=3), A352050 (k=4), A352051 (k=5), A352052 (k=6), A352053 (k=7), A352054 (k=8), A352055 (k=9), A352056 (k=10). Cf. A006519, A050999, A076577, A233091. Sequence in context: A019571 A008024 A008056 * A206920 A108612 A065741 Adjacent sequences: A352045 A352046 A352047 * A352049 A352050 A352051 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Mar 01 2022 STATUS approved

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Last modified March 4 16:26 EST 2024. Contains 370532 sequences. (Running on oeis4.)