cp's OEIS Frontend

A330902 Odd numbers k such that s(k) = s(k+2), where s(k) is Schemmel's totient function of order 2 (A058026).

%I A330902 #12 May 01 2020 09:58:34
%S A330902 1,9359,23933,97405,131493,304589,529205,6005613,6024473,6057257,
%T A330902 7636517,9566549,11481581,25143017,25439117,28542745,40473869,
%U A330902 57712193,58761197,69502169,77085497,78481397,81127109,95223857,99815303,104092517,112282481,119954477,130052613
%N A330902 Odd numbers k such that s(k) = s(k+2), where s(k) is Schemmel's totient function of order 2 (A058026).
%C A330902 Since s(k) = 0 for all even numbers k, they are trivial solutions of the equation s(k) = s(k+2) and therefore they were excluded from this sequence.
%C A330902 Analogous to A001494 since Schemmel's totient functions are a generalization of the Euler totient function (A000010).
%D A330902 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 276.
%H A330902 Amiram Eldar, <a href="/A330902/b330902.txt">Table of n, a(n) for n = 1..92</a>
%H A330902 Victor Schemmel, <a href="https://doi.org/10.1515/crll.1869.70.191">Ueber relative Primzahlen</a>, Journal für die reine und angewandte Mathematik, Vol. 70 (1869), pp. 191-192.
%e A330902 1 is a term since s(1) = s(3) = 1.
%e A330902 9359 is a term since s(9359) = s(9361) = 6615.
%t A330902 f[p_, e_] := (p-2) * p^(e-1); s[1]=1; s[n_] := Times @@ (f @@@ FactorInteger[n]); seq={}; s1 = 1; Do[s2 = s[n]; If[s1 == s2, AppendTo[seq, n-2]]; s1 = s2, {n, 3, 10^6, 2}]; seq
%Y A330902 Cf. A001494, A058026.
%K A330902 nonn
%O A330902 1,2
%A A330902 _Amiram Eldar_, May 01 2020