A390960 - OEIS

%I #8 Nov 27 2025 00:54:34

%S 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,

%T 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,

%U 5,4,4,2,12,2,2,2,2,10,7,4,2,2,6,2,4,2,2,10

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

%C The nonzero terms in A348341.

%C The sum of these divisors is A390961(n).

%H Amiram Eldar, <a href="/A390960/b390960.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (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, ", ")));}

%Y Cf. A036537, A162643, A348341, A390961.

%Y Cf. A327576, A327839.

%Y Similar sequences: A174961, A390958.

%K nonn,easy

%O 1,3

%A _Amiram Eldar_, Nov 25 2025