A067702 Numbers k such that sigma(k) == 0 (mod k+2).

12, 70, 88, 180, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470, 2251799645913088

Offset: 1

Author

Benoit Cloitre, Feb 05 2002

Keywords

• nonn
• more

Comments

If 2^i-5 is prime for i > 2 then let x = (2^i-5)*2^(i-1). Then sigma(x)=2*(x+2), so x is in the sequence. There are other terms that are not of this form. - Jud McCranie, Jan 12 2019

Contains terms of A088832, terms m of A088834 with (sigma(m)-6)/m = 3, terms m of A045770 with (sigma(m)-8)/m = 4, terms m of A076496 with (sigma(m)-12)/m = 6. - Max Alekseyev, May 26 2025

Examples

			sigma(180) = 546 = 3(180+2), so 180 is in the sequence.
		

Crossrefs

Contains subsequence A088832.

Cf. A045768, A156560, A059608, A045770, A076496, A088834.

Programs

Mathematica

Select[Range[84*10^5],Divisible[DivisorSigma[1,#],#+2]&] (* Harvey P. Dale, May 11 2018 *)

PARI

isok(n) = sigma(n) % (n+2) == 0; \\ Michel Marcus, Nov 22 2013

Extensions

a(9)-a(11) from Michel Marcus, Nov 22 2013

a(12)-a(13) from Jud McCranie, Jan 12 2019

a(14) from Jud McCranie, Jan 13 2019

a(15) from Jud McCranie, Dec 02 2019

a(16) from Max Alekseyev, May 26 2025