A168127 Numbers k such that Sum_{j=1..k} sigma(j) / sigma(k) is an integer.

1, 3, 29, 365, 1225, 81595, 86249, 185699, 582917, 11413204, 16646745763, 311408527843, 709342670921, 881267828693

Offset: 1

Author

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

Keywords

• nonn
• more

Comments

Numbers k such that A024916(k)/A000203(k) is an integer.

Corresponding values of sigma(k), Sum_{j=1..k} sigma(j) and Sum_{j=1..k} sigma(j)/sigma(k) are given in A168129, A168130 and A168128. - Jaroslav Krizek, Nov 21 2009

a(11) > 10^10. - Donovan Johnson, Oct 16 2013

a(15) > 10^12. - Giovanni Resta, Jun 06 2016

Examples

			29 is in the sequence because A024916(29) / A000203(29) = 690 / 30 = 23 is an integer.
		

Crossrefs

Cf. A000203, A024916, A168128, A168129, A168130.

Programs

PARI

m=0; for(k=1, 11413204, s=sigma(k); m=m+s; if(m%s==0, print1(k ", "))) \\ Donovan Johnson, Oct 16 2013

PARI

isok(k) = (sum(j=1, k, sigma(j)) % sigma(k)) == 0; \\ Michel Marcus, Feb 19 2020

Extensions

a(8)-a(10) from Donovan Johnson, Oct 16 2013

a(11)-a(14) from Giovanni Resta, Jun 06 2016

Name edited by Michel Marcus, Feb 19 2020