A348271 a(n) is the sum of noninfinitary divisors of n.

0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 8, 0, 0, 0, 14, 0, 9, 0, 12, 0, 0, 0, 0, 5, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 24, 18, 0, 0, 56, 7, 15, 0, 28, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 24, 42, 0, 0, 0, 36, 0, 0, 0, 45, 0, 0, 20, 40, 0, 0, 0, 84, 39

Offset: 1

Author

Amiram Eldar, Oct 09 2021

Keywords

• nonn

Examples

			a(12) = 8 since 12 has 2 noninfinitary divisors, 2 and 6, and 2 + 6 = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Infinitary Divisor.

Crossrefs

Cf. A000203, A036537, A049417, A077609, A162643, A327633.

Similar sequences: A034448, A048146, A051377, A188999.

Programs

Mathematica

f[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}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; a[n_]:= DivisorSigma[1,n] - isigma[n]; Array[a, 100]

Formula

a(n) = A000203(n) - A049417(n).

a(n) = 0 if and only if the number of divisors of n is a power of 2, (i.e., n is in A036537).

a(n) > 0 if and only if the number of divisors of n is not a power of 2, (i.e., n is in A162643).