The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A033634

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A033634

OddPowerSigma(n) = sum of odd power divisors of n.
(history; published version)

#33 by Joerg Arndt at Thu Oct 27 07:31:52 EDT 2022

STATUS

reviewed

approved

#32 by Michel Marcus at Thu Oct 27 05:25:10 EDT 2022

STATUS

proposed

reviewed

#31 by Amiram Eldar at Thu Oct 27 03:02:58 EDT 2022

STATUS

editing

proposed

#30 by Amiram Eldar at Thu Oct 27 02:58:37 EDT 2022

CROSSREFS

Cf. A000203, A008864, A072587, A181150, A268335, A295316.

#29 by Amiram Eldar at Thu Oct 27 02:58:03 EDT 2022

EXAMPLE

The divisors of 7 are 1^1 and 7^1, which have only odd exponents (=1), so a(8) = 1+7 = 8. The divisors of 8 are 1^1, 2^1, 2^2 and 2^3; 2^2 has an even prime power and does not count, so a(8) = 1+2+8=11. The divisors of 12 are 1^1, 2^1, 3^1, 2^2, 2^1*3^1 and 2^2*3; 2^2 and 2^2*3 don't count because they have prime factors with even powers, so a(12) = 1+2+3+6 = 12.

#28 by Amiram Eldar at Thu Oct 27 02:31:22 EDT 2022

LINKS

<a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.

CROSSREFS

Cf. A000203, A008864, A181150, A268335, A295316.

#27 by Amiram Eldar at Thu Oct 27 02:30:36 EDT 2022

FORMULA

Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/12) * Product_{p prime} (1 - 1/(p*(p+1))) = A072691 * A065463 = 0.5793804... . - Amiram Eldar, Oct 27 2022

CROSSREFS

Cf. A065463, A072691.

STATUS

approved

editing

#26 by Alois P. Heinz at Tue May 14 10:03:04 EDT 2019

STATUS

proposed

approved

#25 by Amiram Eldar at Tue May 14 09:48:38 EDT 2019

STATUS

editing

proposed

#24 by Amiram Eldar at Tue May 14 09:48:14 EDT 2019

MATHEMATICA

f[e_] := If[OddQ[e], e+2, e+1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); a[1] = 1; a[n_] := Times @@ (fun @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, May 14 2019 *)

STATUS

approved

editing