A015865 Numbers k such that sigma(k) = sigma(k+5).

6, 46, 1030, 2673, 4738, 4785, 10437, 14025, 20038, 20326, 23914, 28702, 31101, 39273, 39669, 41349, 41554, 44709, 46366, 55918, 68638, 74205, 93682, 94365, 96790, 103678, 115245, 115642, 124785, 169990, 182830, 185073, 207118, 214090

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

Using the method proposed by Guy and Shanks to construct solutions of sigma(k) = sigma(k + 1), it is possible to search for large terms of this sequence: If q = 3^(m+1) + 8 and p = (3^m*q - 5)/2 are primes, then 2*p is a term. This occurs for m = 0, 1 and 4, giving the terms 6, 46 and 20326. If q = 3^(m+1) - 22 and p = (3^m*q + 5)/2 are primes, then 3^m*q is a term. This occurs for m = 45 giving the term 26183890704263137277609197558886063678754201. In both cases there are no other solutions for m <= 10^4. - Amiram Eldar, May 29 2020

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• Richard Guy and Daniel Shanks, A Constructed Solution of sigma(n) = sigma(n+1), The Fibonacci Quarterly, Vol. 12, No. 3 (1974), p. 299.

Crossrefs

Cf. A000203, A002961, A007373, A015861, A015863, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647.

Programs

Mathematica

Select[Range[215000], DivisorSigma[1, #]==DivisorSigma[1, # + 5] &] (* Vincenzo Librandi, Mar 10 2014 *)
Position[Partition[DivisorSigma[1,Range[215000]],6,1],?(#[[1]] == #[[6]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, Sep 18 2021 *)

PARI

is(n)=sigma(n)==sigma(n+5) \\ Charles R Greathouse IV, Mar 09 2014

Extensions

Corrected and extended by T. D. Noe, Oct 31 2006