OFFSET

1,1

COMMENTS

Terms of this sequence are totients selected by prime replicators of totients not terms of this sequence.

A303747 a restriction of this sequence gives a relation T = (P * TS) - TS where T is a term, P is the corresponding prime replicator and TS is the starting or seed totient. The relation fails for a(202) = 1210. 1210 does not equal (11 * a(19)) - a(19), i.e., (11 * 110) - 110.

For known terms, the greatest common divisor of the solutions of a(n) is either a power of the largest prime factor of solutions of a(n), or is evenly divisible by same.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Max Alekseyev, PARI scripts for various problems

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.

EXAMPLE

10 is a term because the largest prime factor of 11 and 22, the solutions of phi(10) is 11.

2 is not a term because there is no common largest prime factor of 3, 4 and 6, the solutions of phi(2).

MAPLE

filter:= proc(n) local L, q;

L:= numtheory:-invphi(n);

if nops(L) = 0 then return false fi;

q:= max(numtheory:-factorset(L[1]));

andmap(t -> max(numtheory:-factorset(t))=q, L[2..-1]);

end proc:

select(filter, [seq(i, i=2..1000, 2)]); # Robert Israel, Jun 25 2018

PROG

(PARI) isok(n) = if (n > 1, #Set(apply(x->vecmax(factor(x)[, 1]), invphi(n))) == 1); \\ Michel Marcus, May 13 2018

CROSSREFS

KEYWORD

nonn

AUTHOR

Torlach Rush, Apr 29 2018

STATUS

approved