A305726 Totients t the solutions of which cannot be divided by a prime to yield the solutions of a totient < t.

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, 48, 54, 60, 64, 72, 80, 84, 88, 96, 100, 108, 112, 120, 128, 132, 144, 156, 160, 162, 168, 176, 180, 192, 200, 216, 220, 224, 232, 240, 252, 256, 264, 272, 276, 280, 288, 294, 300, 312, 320, 324, 336, 342, 348, 352, 360, 384, 396, 400

Offset: 1

Author

Torlach Rush, Jun 21 2018

Keywords

• nonn

Comments

This sequence is the complement of A303746.

Examples

			1 is a term because there is no prime that divides the solutions of phi(x) = 1 (1 and 2).
2 is a term because there is no prime that divides the solutions of phi(x) = 2 (3, 4, and 6).
10 is not a term because 11 divides solutions of phi(x) = 10 (11 and 22) yielding 1 and 2 the solutions of phi(x) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (for invphi pari script).
• K. B. Stolarski and S. Greenbaum, A Ratio Associated with phi(x) = n, The Fibonacci Quarterly, Volume 23, Number 3, August 1985, pp. 265-269.

Crossrefs

Cf. A000010, A085713, A303746.

Programs

PARI

isok(n) = {if (istotient(n), v = invphi(n); g = gcd(v); if (g == 1, return (1)); f = factor(g); for (k=1, #f~, vv = v/f[k,1]; nt = eulerphi(vv[1]); if (vv == invphi(nt), return(0));); return (1););} \\ Michel Marcus, Jul 25 2018