A345943 -id:A345943

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page 1

A345941

a(n) = gcd(n, A329044(n)).

+10
6

1, 2, 3, 4, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 4, 17, 9, 19, 5, 7, 11, 23, 3, 25, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 9, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 25, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 7, 4, 13, 11, 67, 17, 23, 7, 71, 9, 73, 37, 25, 19, 11, 13, 79, 5, 3, 41, 83, 7, 17, 43, 29, 11, 89

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Only powers of primes (A000961) occur as terms. A346087 gives the exponents. - Antti Karttunen, Jul 07 2021

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

FORMULA

a(n) = gcd(n, A329044(n)).

a(n) = n / A345942(n).

a(n) = A329044(n) / A345943(n).

a(p) = p for all primes p.

From Antti Karttunen, Jul 07 2021: (Start)

a(n) = A006530(n)^A346087(n) = A006530(n)^min(A071178(n), A329348(n)).

a(n) = gcd(n, A346097(n)).

A006530(a(n)) = A020639(A329044(n)) = A006530(n).

(End)

PROG

(PARI) A345941(n) = gcd(n, A329044(n)); \\ Rest of program given in A329044.

CROSSREFS

Cf. A000961, A006530, A020639, A071178, A108951, A324886, A329348, A329044, A345942, A345943, A346087, A346097.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 03 2021

STATUS

approved

A345942

a(n) = n / gcd(n, A329044(n)).

+10
3

1, 1, 1, 1, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 3, 4, 1, 2, 1, 4, 3, 2, 1, 8, 1, 2, 9, 4, 1, 6, 1, 16, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 7, 2, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 9, 16, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 16, 27, 2, 1, 12, 5, 2, 3, 8, 1, 18, 7, 4, 3, 2, 5, 32, 1, 2, 9, 20, 1, 6