A263085 Partial sums of A099774 (A099774(n) = number of divisors of n-th odd number).

1, 3, 5, 7, 10, 12, 14, 18, 20, 22, 26, 28, 31, 35, 37, 39, 43, 47, 49, 53, 55, 57, 63, 65, 68, 72, 74, 78, 82, 84, 86, 92, 96, 98, 102, 104, 106, 112, 116, 118, 123, 125, 129, 133, 135, 139, 143, 147, 149, 155, 157, 159, 167, 169, 171, 175, 177, 181, 187, 191, 194, 198

Offset: 1

Author

Antti Karttunen, Oct 12 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10082

Crossrefs

Cf. A000005, A001620, A006218, A099774, A263084, A263086.

Programs

Mathematica

FoldList[DivisorSigma[0,2*#2-1]+#1&,1,Range[2,62]] (* Ivan N. Ianakiev, Oct 24 2015 *)
Accumulate[Table[DivisorSigma[0, 2*n-1], {n, 1, 100}]] (* Vaclav Kotesovec, Jan 14 2019 *)

PARI

lista(nn) = {s = 0; forstep (n=1, nn, 2, s += numdiv(n); print1(s, ", "););} \\ Michel Marcus, Oct 12 2015

Formula

a(1) = 1; for n > 1, a(n) = A000005(2*n-1) + a(n-1).

a(n) = A263086(n) - A263084(n).

a(n) ~ n * (log(n) + 2*gamma + 3*log(2) - 1)/2, where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 14 2024