A379379 Sum of odd divisors of n except the "e" odd divisors described in A005279.

1, 1, 4, 1, 6, 1, 8, 1, 13, 6, 12, 1, 14, 8, 19, 1, 18, 1, 20, 1, 32, 12, 24, 1, 31, 14, 40, 1, 30, 1, 32, 1, 48, 18, 41, 1, 38, 20, 56, 1, 42, 1, 44, 12, 49, 24, 48, 1, 57, 31, 72, 14, 54, 1, 72, 1, 80, 30, 60, 1, 62, 32, 95, 1, 84, 1, 68, 18, 96, 41, 72, 1, 74

Offset

1,3

Comments

Shares infinitely many terms with A000593.

a(n) = A000593(n) if n is not in A005279.

a(n) < A000593(n) if n is in A005279.

Conjectures from Omar E. Pol, Aug 27 2025: (Start)

a(n) is the sum of the smallest numbers of the 2-dense sublists of divisors of n.

a(n) is the sum of the divisors p of n such that p is greater than twice the adjacent previous divisor of n. (End)

Links

Table of n, a(n) for n=1..73.

Formula

Conjectures from Omar E. Pol, Oct 30 2025: (Start)

a(n) = A000593(n) - A383147(n).

a(n) = A000203(n) - A389591(n). (End)

Mathematica

a[n_] := Module[{d = Partition[Divisors[n], 2, 1]}, 1 + Total[Select[d, OddQ[#[[2]]] && #[[2]] >= 2*#[[1]] &][[;; , 2]]]]; Array[a, 100] (* Amiram Eldar, Dec 22 2024 *)

Crossrefs

Row sums of A379288.

Cf. A001227, A000593, A005279, A182469, A237270, A237271, A237593, A239657, A379374, A379384, A379461, A383147, A389591.

Sequence in context: A354254 A215619 A136706 * A326478 A324118 A100796

Adjacent sequences: A379376 A379377 A379378 * A379380 A379381 A379382

Keyword

nonn

Author

Omar E. Pol, Dec 21 2024

Extensions

More terms from Alois P. Heinz, Dec 22 2024

Status

approved