A390961 The sum of the noninfinitary divisors of the numbers whose number of divisors is not a power of 2 (A162643).

2, 3, 8, 14, 9, 12, 5, 16, 12, 41, 24, 18, 56, 7, 15, 28, 48, 24, 42, 36, 45, 20, 40, 84, 39, 64, 54, 48, 48, 21, 36, 87, 80, 112, 60, 42, 11, 64, 72, 96, 96, 233, 28, 76, 60, 54, 112, 72, 117, 84, 13, 60, 88, 40, 168, 246, 96, 168, 149, 108, 75, 144, 72, 196, 108

Offset

1,1

Comments

The nonzero terms in A348271.

The number of these divisors is A390960(n).

Links

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

Formula

a(n) = A348271(A162643(n)).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (A072691 - A327574) / (1 - A327839)^2 = 0.94147775598464357187... .

Mathematica

f1[p_, e_] := (p^(e+1) - 1)/(p - 1);
f2[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]];
s[1] = 0; s[n_] := Module[{f = FactorInteger[n]}, Times @@ f1 @@@ f - Times @@ f2 @@@ f]
Select[Array[s, 300], # > 0 &]

Prog

(PARI) list(kmax) = {my(f, s, d); for(k = 1, kmax, f = factor(k); s = sigma(f) - prod(i = 1, #f~, d = binary(f[i, 2]); prod(k = 1, #d, if(d[k], 1 + f[i, 1]^(2^(#d-k)), 1))); if(s > 0, print1(s, ", "))); }

Crossrefs

Cf. A036537, A162643, A348271, A390960.

Cf. A072691, A327574, A327839.

Similar sequences: A368038, A390959.

Sequence in context: A145929 A153865 A369774 * A331820 A368855 A022951

Adjacent sequences: A390958 A390959 A390960 * A390962 A390963 A390964

Keyword

nonn,easy

Author

Amiram Eldar, Nov 25 2025

Status

approved