A168129 Numbers sigma(k) when Sum_(j=1..k) sigma(j) / sigma(k) is an integer.

1, 4, 30, 444, 1767, 86250, 97920, 185700, 584640, 21954842, 17654544432, 357550809280, 709346653572, 1061551370880

Offset: 1

Author

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

Keywords

• nonn
• more

Comments

Numbers A000203(k) when A024916(k) / A000203(k) is an integer.

Corresponding values of k, Sum_(j=1..k) sigma(k) and Sum_(j=1..k) sigma(j)/sigma(k) are given in A168127, A168130 and A168128. - Jaroslav Krizek, Nov 21 2009

Examples

			a(3) = 30 because A024916(29) / A000203(29) = 690 / 30 = 23 is an integer, where 29 is A168127(3).
		

Crossrefs

Cf. A000203, A024916, A168127, A168128, A168130.

Programs

PARI

v=vector(10); c=0; m=0; for(k=1, 11413204, s=sigma(k); m=m+s; if(m%s==0, c++; v[c]=s)); v=vecsort(v); for(i=1, c, print1(v[i] ", ")) \\ Donovan Johnson, Oct 16 2013

Formula

a(n) = A000203(A168127(n)). - Michel Marcus, Feb 22 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 22 2020