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

1,2

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).

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.

Example

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

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

Crossrefs

Cf. A001494, A058026.

Sequence in context: A228519 A292283 A265457 * A323803 A246736 A289858

Adjacent sequences: A330899 A330900 A330901 * A330903 A330904 A330905

Keyword

nonn

Author

Amiram Eldar, May 01 2020

Status

approved