

A303746


Totients t for which {x: phi(x)=t} share the same largest prime factor.


3



10, 22, 28, 30, 44, 46, 52, 54, 56, 58, 66, 70, 78, 82, 92, 102, 104, 106, 110, 116, 126, 130, 136, 138, 140, 148, 150, 164, 166, 172, 178, 184, 190, 196, 198, 204, 208, 210, 212, 222, 226, 228, 238, 250, 260, 262, 268, 270, 282, 292, 294, 296, 306, 310, 316, 328, 330
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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. 265269.


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

Cf. A000010, A002202, A085713.
Subsequence of A303745.
Sequence in context: A063555 A228010 A303745 * A303747 A007366 A302280
Adjacent sequences: A303743 A303744 A303745 * A303747 A303748 A303749


KEYWORD

nonn


AUTHOR

Torlach Rush, Apr 29 2018


STATUS

approved



