A390959 The sum of the non-bi-unitary divisors of the numbers that are not exponentially odd.

2, 3, 8, 4, 9, 12, 5, 16, 41, 24, 18, 16, 7, 15, 28, 48, 24, 8, 36, 45, 20, 40, 24, 9, 64, 54, 48, 21, 36, 87, 80, 32, 60, 42, 11, 64, 72, 96, 96, 133, 28, 76, 60, 54, 112, 27, 84, 13, 60, 88, 40, 48, 246, 96, 32, 149, 108, 75, 144, 72, 56, 108, 144, 143, 160, 126

Offset

1,1

Comments

The nonzero terms in A319072.

The number of these divisors is A390958(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A319072(A072587(n)).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (A072691 - A307160)/(1 - A065463)^2 = 0.79707813708656709254... .

Mathematica

f1[p_, e_] := (p^(e+1) - 1)/(p - 1); f2[p_, e_] := f1[p, e] - If[OddQ[e], 0, p^(e/2)]; s[1] = 0; s[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct; Select[Array[s, 300], # > 0 &]

Prog

(PARI) list(kmax) = {my(f); for(k = 1, kmax, f = factor(k); if(vecprod(apply(x -> x%2, f[, 2])) == 0, print1(sigma(f) - prod(i = 1, #f~, (f[i, 1]^(f[i, 2]+1)-1)/(f[i, 1]-1) - if(!(f[i, 2] % 2), f[i, 1]^(f[i, 2]/2))), ", "))); }

Crossrefs

Cf. A072587, A268335, A319072, A390958.

Cf. A065463, A072691, A307160.

Similar sequences: A368038, A390961.

Sequence in context: A110142 A158928 A198369 * A193731 A193975 A224665

Adjacent sequences: A390956 A390957 A390958 * A390960 A390961 A390962

Keyword

nonn,easy

Author

Amiram Eldar, Nov 25 2025

Status

approved