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

%I A305726 #27 Jan 05 2025 19:51:41
%S A305726 1,2,4,6,8,12,16,18,20,24,32,36,40,42,48,54,60,64,72,80,84,88,96,100,
%T A305726 108,112,120,128,132,144,156,160,162,168,176,180,192,200,216,220,224,
%U A305726 232,240,252,256,264,272,276,280,288,294,300,312,320,324,336,342,348,352,360,384,396,400
%N A305726 Totients t the solutions of which cannot be divided by a prime to yield the solutions of a totient < t.
%C A305726 This sequence is the complement of A303746.
%H A305726 Amiram Eldar, <a href="/A305726/b305726.txt">Table of n, a(n) for n = 1..10000</a>
%H A305726 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (for invphi pari script).
%H A305726 K. B. Stolarski and S. Greenbaum, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/23-3/stolarsky.pdf">A Ratio Associated with phi(x) = n</a>, The Fibonacci Quarterly, Volume 23, Number 3, August 1985, pp. 265-269.
%e A305726 1 is a term because there is no prime that divides the solutions of phi(x) = 1 (1 and 2).
%e A305726 2 is a term because there is no prime that divides the solutions of phi(x) = 2 (3, 4, and 6).
%e A305726 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.
%o A305726 (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
%Y A305726 Cf. A000010, A085713, A303746.
%K A305726 nonn
%O A305726 1,2
%A A305726 _Torlach Rush_, Jun 21 2018