This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A264740 #25 Jun 26 2025 13:34:56
%S A264740 1,2,4,3,6,8,8,4,13,12,12,12,14,16,24,5,18,26,20,18,32,24,24,16,31,28,
%T A264740 40,24,30,48,32,6,48,36,48,39,38,40,56,24,42,64,44,36,78,48,48,20,57,
%U A264740 62,72,42,54,80,72,32,80,60,60,72,62,64,104,7
%N A264740 Sum of odd parts of divisors of n.
%C A264740 It is easy to show that a(n) is odd iff n is a square.
%C A264740 a(n) = sigma(n) for odd n, since any divisor of an odd number is odd.
%C A264740 Inverse Möbius transform of A000265(n). - _Wesley Ivan Hurt_, Jun 26 2025
%H A264740 Reinhard Zumkeller, <a href="/A264740/b264740.txt">Table of n, a(n) for n = 1..10000</a>
%F A264740 Multiplicative with a(2^k) = k + 1, a(p^k) = sigma(p^k) = (p^(k+1)-1) / (p-1) for p > 2.
%F A264740 Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/18 = 0.548311... (A086463). - _Amiram Eldar_, Nov 04 2022
%F A264740 a(n) = Sum_{d|n} A000265(d). - _Ridouane Oudra_, Oct 30 2023
%e A264740 Divisors of 10 are 1, 2, 5, 10. The odd parts of these are 1, 1, 5, 5, so a(10) = 1+1+5+5 = 12.
%p A264740 with(numtheory): with(padic): seq(add(d/2^ordp(d,2), d in divisors(n)), n=1..80); # _Ridouane Oudra_, Oct 30 2023
%t A264740 f[p_, e_] := If[p == 2, e + 1, (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Jun 30 2020 *)
%o A264740 (PARI) a(n)=my(k=valuation(n,2));sigma(n)\(2^(k+1)-1)*(k+1)
%o A264740 (Haskell)
%o A264740 a264740 = sum . map a000265 . a027750_row'
%o A264740 -- _Reinhard Zumkeller_, Nov 23 2015
%Y A264740 Cf. A000593, A000265, A000203.
%Y A264740 Cf. A027750, A086463.
%K A264740 nonn,look,mult
%O A264740 1,2
%A A264740 _Franklin T. Adams-Watters_, Nov 22 2015