cp's OEIS Frontend

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

%I A263085 #23 Jan 14 2024 02:26:20
%S A263085 1,3,5,7,10,12,14,18,20,22,26,28,31,35,37,39,43,47,49,53,55,57,63,65,
%T A263085 68,72,74,78,82,84,86,92,96,98,102,104,106,112,116,118,123,125,129,
%U A263085 133,135,139,143,147,149,155,157,159,167,169,171,175,177,181,187,191,194,198
%N A263085 Partial sums of A099774 (A099774(n) = number of divisors of n-th odd number).
%H A263085 Antti Karttunen, <a href="/A263085/b263085.txt">Table of n, a(n) for n = 1..10082</a>
%F A263085 a(1) = 1; for n > 1, a(n) = A000005(2*n-1) + a(n-1).
%F A263085 a(n) = A263086(n) - A263084(n).
%F A263085 a(n) ~ n * (log(n) + 2*gamma + 3*log(2) - 1)/2, where gamma is Euler's constant (A001620). - _Amiram Eldar_, Jan 14 2024
%t A263085 FoldList[DivisorSigma[0,2*#2-1]+#1&,1,Range[2,62]] (* _Ivan N. Ianakiev_, Oct 24 2015 *)
%t A263085 Accumulate[Table[DivisorSigma[0, 2*n-1], {n, 1, 100}]] (* _Vaclav Kotesovec_, Jan 14 2019 *)
%o A263085 (Scheme, with memoization-macro definec)
%o A263085 (definec (A263085 n) (if (= 1 n) (A099774 n) (+ (A099774 n) (A263085 (- n 1)))))
%o A263085 (PARI) lista(nn) = {s = 0; forstep (n=1, nn, 2, s += numdiv(n); print1(s, ", "););} \\ _Michel Marcus_, Oct 12 2015
%Y A263085 Cf. A000005, A001620, A006218, A099774, A263084, A263086.
%K A263085 nonn
%O A263085 1,2
%A A263085 _Antti Karttunen_, Oct 12 2015