

A342916


a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{pn, p prime} (1 + 1/p).


4



2, 1, 1, 5, 1, 7, 1, 3, 5, 11, 1, 13, 1, 5, 2, 17, 1, 19, 1, 7, 11, 23, 1, 25, 13, 9, 7, 29, 1, 31, 1, 11, 17, 35, 3, 37, 1, 13, 5, 41, 1, 43, 1, 5, 23, 47, 1, 49, 25, 17, 13, 53, 1, 55, 7, 19, 29, 59, 1, 61, 1, 21, 2, 65, 11, 67, 1, 23, 35, 71, 1, 73, 1, 25, 19, 77, 13, 79, 1, 9, 41, 83, 1, 85, 43, 29, 11, 89, 1, 91, 23, 31
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OFFSET

1,1


COMMENTS

It is conjectured that a(n) = 1 only when n is a prime, A000040. See Thomas Ordowski's May 21 2017 problem in A001615.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384


FORMULA

a(n) = (1+n) / A342915(n) = (1+n) / gcd(1+n, A001615(n)).


PROG

(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]1))); \\ After code in A001615
A342916(n) = ((1+n)/gcd(1+n, A001615(n)));


CROSSREFS

Cf. A000040, A001615, A342915, A342917.
Cf. also A160596.
After n=1 differs from A342918 for the first time at n=44, where a(44) = 5, while A342918(44) = 15.
Sequence in context: A210876 A174785 A136789 * A339966 A022661 A120292
Adjacent sequences: A342913 A342914 A342915 * A342917 A342918 A342919


KEYWORD

nonn


AUTHOR

Antti Karttunen, Mar 29 2021


EXTENSIONS

Incorrect Anumber in the formula corrected by Antti Karttunen, May 31 2021


STATUS

approved



