A306695 - OEIS

The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

A306695

a(n) = gcd(n, psi(n)).

1, 1, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 8, 1, 18, 1, 4, 1, 2, 1, 24, 5, 2, 9, 4, 1, 6, 1, 16, 3, 2, 1, 36, 1, 2, 1, 8, 1, 6, 1, 4, 9, 2, 1, 48, 7, 10, 3, 4, 1, 54, 1, 8, 1, 2, 1, 12, 1, 2, 3, 32, 1, 6, 1, 4, 3, 2, 1, 72, 1, 2, 15, 4, 1, 6, 1, 16, 27, 2, 1, 12, 1, 2, 3, 8, 1, 18, 7, 4, 1, 2, 5, 96, 1, 14, 9, 20 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,4`
	COMMENTS	`Here psi(n) is Dedekind's psi function A001615.` `a(n) <= n <= A001615(n).` `a(n) = n iff a(n) * 2 = A001615(n), n > 1.` `a(n) = 1 iff either n=2 or n is in A255602. - Robert Israel, Mar 12 2019`
	LINKS	`Robert Israel, Table of n, a(n) for n = 1..10000` `Wikipedia, Dedekind psi function`
	FORMULA	`a(n) = gcd(n, A001615(n)).`
	MAPLE	`f:= proc(n) local p; igcd(n, n*mul(1+1/p, p=numtheory:-factorset(n))) end proc:` `map(f, [$1..100]); # Robert Israel, Mar 11 2019`
	PROG	`(PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615` `a(n) = gcd(n, dpsi(n)); \\ Michel Marcus, Mar 05 2019`
	CROSSREFS	`Cf. A001615, A255602.` `Sequence in context: A154744 A285038 A243145 * A242926 A189733 A306927` `Adjacent sequences: A306692 A306693 A306694 * A306696 A306697 A306698`
	KEYWORD	`nonn`
	AUTHOR	`Torlach Rush, Mar 05 2019`
	STATUS	`approved`

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)