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

1, 9359, 23933, 97405, 131493, 304589, 529205, 6005613, 6024473, 6057257, 7636517, 9566549, 11481581, 25143017, 25439117, 28542745, 40473869, 57712193, 58761197, 69502169, 77085497, 78481397, 81127109, 95223857, 99815303, 104092517, 112282481, 119954477, 130052613

Offset: 1

Author

Amiram Eldar, May 01 2020

Keywords

• nonn

Comments

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.

Analogous to A001494 since Schemmel's totient functions are a generalization of the Euler totient function (A000010).

Examples

			1 is a term since s(1) = s(3) = 1.
9359 is a term since s(9359) = s(9361) = 6615.
		

References

• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 276.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..92
• Victor Schemmel, Ueber relative Primzahlen, Journal für die reine und angewandte Mathematik, Vol. 70 (1869), pp. 191-192.

Crossrefs

Cf. A001494, A058026.

Programs

Mathematica

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