cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

Keywords

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

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

A168128 Numbers Sum_(j=1..k) sigma(j) / sigma(k) when this expression is an integer.

Original entry on oeis.org

1, 2, 23, 247, 699, 55921, 70936, 152730, 478017, 4879815, 12909834588, 223070292558, 583407686653, 601718433498
Offset: 1

Views

Author

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

Keywords

Comments

Numbers A024916(k)/A000203(k) when it is an integer.
Corresponding values of k, sigma(k) and Sum_(j=1..k) sigma(j) are given in A168127, A168129 and A168130. - Jaroslav Krizek, Nov 21 2009

Examples

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

Crossrefs

Programs

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

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

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

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

Keywords

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

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
Showing 1-3 of 3 results.