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 1-2 of 2 results.

A076374 Smallest solution to x+n*phi(x) = sigma(x) = x+n*A000010(x) = A000203(x).

Original entry on oeis.org

2, 10, 6, 12, 9888, 90, 672, 37680, 3422877696, 159840, 35640, 2977920, 61724520, 9530611200, 272065167360, 613958400
Offset: 1

Views

Author

Labos Elemer, Oct 15 2002

Keywords

Comments

See comment to A076373.
a(17) > 10^12. a(18) > 10^12. a(19) = 353928960. - Donovan Johnson, Feb 29 2012
a(17) > 10^13. a(18) > 10^13. - Giovanni Resta, Apr 24 2016

Examples

			n=3:solution set = {6,89152,..?}; n=7:solution-set = {672,146412,179864,..?}

Crossrefs

Cf. A000010, A000203, A076373.

Extensions

a(8) corrected and a(9), a(12)-a(16) from Donovan Johnson, Feb 29 2012

A136541 Numbers n such that sum of the proper divisors of n is equal to (3/4)*phi(n).

Original entry on oeis.org

33, 2889, 235953, 19129689
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 08 2008

Keywords

Comments

If m>0 and p=4*3^m-1 is prime(m is in the sequence A005540) then n=3^m*p is in the sequence. Because sigma(n)-n=(1/2)*(3^(m+1)-1) *4*3^m-3^m*(4*3^m-1)=3^m*(2*3^m-1)=(3/4)*(2*3^(m-1))*((4*3^m-1)-1) =(3/4)*phi(3^m)*phi(p)=(3/4)*phi(3^m*p)=(3/4)*phi(n). The first four terms of the sequence are of such form if the 5th term is also of such form then it is equal to 823564514029689. Next term is greater than 2*10^9. Is it true that all terms are of the mentioned form?
a(5) > 10^12. - Giovanni Resta, Nov 03 2012

Examples

			sigma(33)-33=48-33=15=(3/4)*20=(3/4)*phi(33).

Crossrefs

Cf. A005540, A076373.

Programs

  • Mathematica
    Do[If[DivisorSigma[1,n]-n==3/4*EulerPhi@n,Print[n]],{n,2000000000}]

Formula

For n=1,2,3 & 4 a(n)=3^(2n-1)*(4*3^(2n-1)-1).
Showing 1-2 of 2 results.

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