A002659 a(n) = 2*sigma(n) - 1.

1, 5, 7, 13, 11, 23, 15, 29, 25, 35, 23, 55, 27, 47, 47, 61, 35, 77, 39, 83, 63, 71, 47, 119, 61, 83, 79, 111, 59, 143, 63, 125, 95, 107, 95, 181, 75, 119, 111, 179, 83, 191, 87, 167, 155, 143, 95, 247, 113, 185, 143, 195, 107, 239, 143, 239, 159, 179, 119, 335, 123, 191

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• easy
• nonn

References

• P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116. Collected Papers, MIT Press, 1978, Vol. I, pp. 1364-1367.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• N. J. A. Sloane, Transforms
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A002660, A002791, A074400.

A row of the array in A242639.

Programs

Mathematica

2DivisorSigma[1,Range[70]]-1 (* Harvey P. Dale, Apr 14 2014 *)

PARI

a(n)=if(n<1,0,2*sigma(n)-1)

Formula

G.f. for Moebius transf.: (x + 2x^2 - x^3 ) / (1 - x )^2.

a(n) = A074400(n) - 1. - Filip Zaludek, Oct 30 2016

Extensions

Better definition from Ralf Stephan, Nov 18 2004