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A263085
Partial sums of A099774 (A099774(n) = number of divisors of n-th odd number).
5
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2015
STATUS
approved