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

%I A015865 #33 Jan 05 2025 19:51:34
%S A015865 6,46,1030,2673,4738,4785,10437,14025,20038,20326,23914,28702,31101,
%T A015865 39273,39669,41349,41554,44709,46366,55918,68638,74205,93682,94365,
%U A015865 96790,103678,115245,115642,124785,169990,182830,185073,207118,214090
%N A015865 Numbers k such that sigma(k) = sigma(k+5).
%C A015865 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
%H A015865 Donovan Johnson, <a href="/A015865/b015865.txt">Table of n, a(n) for n = 1..1000</a>
%H A015865 Richard Guy and Daniel Shanks, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-3/guy.pdf">A Constructed Solution of sigma(n) = sigma(n+1)</a>, The Fibonacci Quarterly, Vol. 12, No. 3 (1974), p. 299.
%t A015865 Select[Range[215000], DivisorSigma[1, #]==DivisorSigma[1, # + 5] &] (* _Vincenzo Librandi_, Mar 10 2014 *)
%t A015865 Position[Partition[DivisorSigma[1,Range[215000]],6,1],_?(#[[1]] == #[[6]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Sep 18 2021 *)
%o A015865 (PARI) is(n)=sigma(n)==sigma(n+5) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A015865 Cf. A000203, A002961, A007373, A015861, A015863, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647.
%K A015865 nonn
%O A015865 1,1
%A A015865 _Robert G. Wilson v_
%E A015865 Corrected and extended by _T. D. Noe_, Oct 31 2006