A390960 The number of noninfinitary divisors of the numbers whose number of divisors is not a power of 2 (A162643).

1, 1, 2, 3, 2, 2, 1, 2, 2, 5, 2, 2, 6, 1, 2, 2, 4, 2, 3, 2, 4, 2, 2, 6, 3, 4, 4, 2, 4, 2, 2, 5, 4, 6, 2, 2, 1, 2, 4, 4, 4, 11, 2, 2, 4, 2, 4, 4, 6, 2, 1, 2, 2, 2, 6, 10, 2, 6, 5, 4, 4, 4, 2, 6, 2, 4, 4, 5, 4, 4, 2, 12, 2, 2, 2, 2, 10, 7, 4, 2, 2, 6, 2, 4, 2, 2, 10

Offset

1,3

Comments

The nonzero terms in A348341.

The sum of these divisors is A390961(n).

Links

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

Formula

a(n) = A348341(A162643(n)).

Sum_{k=1..n} a(k) ~ c * n * log(n), where c = (1 - 2 * A327576) / (1 - A327839) = 0.85449275005462574627... .

Mathematica

s[1] = 0; s[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ (e + 1) - Times @@ (2^DigitCount[#, 2, 1] & /@ e)]; Select[Array[s, 300], # > 0 &]

Prog

(PARI) list(kmax) = {my(f, d); for(k = 1, kmax, f = factor(k); d = numdiv(f) - vecprod(apply(x -> 1 << hammingweight(x), f[, 2])); if(d > 0, print1(d, ", "))); }

Crossrefs

Cf. A036537, A162643, A348341, A390961.

Cf. A327576, A327839.

Similar sequences: A174961, A390958.

Sequence in context: A186037 A144365 A152197 * A049342 A112966 A286657

Adjacent sequences: A390957 A390958 A390959 * A390961 A390962 A390963

Keyword

nonn,easy

Author

Amiram Eldar, Nov 25 2025

Status

approved