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

1,2

Links

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

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

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 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A263085 n) (if (= 1 n) (A099774 n) (+ (A099774 n) (A263085 (- n 1)))))
(PARI) lista(nn) = {s = 0; forstep (n=1, nn, 2, s += numdiv(n); print1(s, ", "); ); } \\ Michel Marcus, Oct 12 2015

Crossrefs

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

Sequence in context: A033035 A047390 A184653 * A206334 A184741 A020959

Adjacent sequences: A263082 A263083 A263084 * A263086 A263087 A263088

Keyword

nonn

Author

Antti Karttunen, Oct 12 2015

Status

approved