A301868 Numbers k such that phi(k, 2) = phi(k+1, 2), where phi(k, 2) = A002472(k).

1, 2, 9, 34, 50, 153, 274, 321, 2841, 4610, 7474, 8254, 10250, 13430, 22149, 38961, 51981, 86845, 91310, 198057, 237325, 367629, 374541, 394834, 419169, 489445, 513890, 516350, 519230, 570230, 717969, 1308609, 1523630, 1557909, 1753730, 1935362, 2109969, 3005409

Offset: 1

Author

Amiram Eldar, Mar 28 2018

Keywords

• nonn

Examples

			phi(9, 2) = phi(10, 2) = 3, thus 9 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200
• Henry L. Alder, A Generalization of the Euler phi-Function, The American Mathematical Monthly, Vol. 65, No. 9 (Nov., 1958), pp. 690-692.

Crossrefs

Cf. A002472.

Programs

Mathematica

seq = {}; a[n_] := If[Head[r = Reduce[GCD[x, n] == 1 && GCD[x + 2, n] == 1 && 1 <= x <= n, x, Integers]] === Or, Length[r], 1]; a0 = a[1]; Do[
a1 = a[k + 1]; If[a1 == a0, AppendTo[seq, k]]; a0 = a1, {k, 1, 1000}]; seq (* after Jean-François Alcover at A002472 *)

PARI

f(n) = sum(x=1, n, (gcd(n, x) == 1) && (gcd(n, x+2) == 1));
isok(n) = f(n) == f(n+1); \\ Michel Marcus, Apr 09 2018

Extensions

a(20)-a(29) from Robert Price, May 18 2018

More terms from Amiram Eldar, Mar 26 2023