A081863 Largest integer m such that m divides (sigma_(2n+1)(2k-1)-sigma(2k-1)) for all k>=1.

24, 240, 168, 480, 264, 21840, 24, 16320, 3192, 2640, 552, 43680, 24, 6960, 57288, 32640, 24, 15353520, 24, 216480, 7224, 5520, 1128, 1485120, 264, 12720, 3192, 13920, 1416, 454293840, 24, 65280, 258888, 240, 18744, 2241613920, 24, 240, 13272, 7360320, 1992

Offset: 1

Author

Benoit Cloitre, Apr 12 2003

Keywords

• nonn

Comments

a(n)==0 mod 24. It seems that a(n)==0 (mod 2n+1) if and only if 2n+1 is an odd prime.

It appears that a(n)=24 for n in A045979, a(n)=168 for n in A051227, a(n)=264 for n in A051229, and a(n)=240 or 480 if n is in A051225. - Michel Marcus, Dec 07 2013

Crossrefs

Cf. A000203.

Programs

PARI

ds(n, k) = sigma(2*k-1, 2*n+1) - sigma(2*k-1);
a(n) = {my(m = ds(n, 1)); for (k=2, 100, m = gcd(m, ds(n, k));); m;} \\ Script computes gcd of 100 terms; for current data, 10 terms are actually sufficient; is there a better way? - Michel Marcus, Dec 07 2013

Extensions

a(12) corrected and more terms from Michel Marcus, Dec 07 2013