A344696 - OEIS

A344696

a(n) = sigma(n) / gcd(sigma(n), A001615(n)).

1, 1, 1, 7, 1, 1, 1, 5, 13, 1, 1, 7, 1, 1, 1, 31, 1, 13, 1, 7, 1, 1, 1, 5, 31, 1, 10, 7, 1, 1, 1, 21, 1, 1, 1, 91, 1, 1, 1, 5, 1, 1, 1, 7, 13, 1, 1, 31, 57, 31, 1, 7, 1, 10, 1, 5, 1, 1, 1, 7, 1, 1, 13, 127, 1, 1, 1, 7, 1, 1, 1, 65, 1, 1, 31, 7, 1, 1, 1, 31, 121, 1, 1, 7, 1, 1, 1, 5, 1, 13, 1, 7, 1, 1, 1, 21, 1, 57, 13

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OFFSET

1,4

COMMENTS

This is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 108 = 4*27, where a(108) = 35, although a(4) = 7 and a(27) = 10. See A344702.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10404

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences related to sigma(n)

FORMULA

a(n) = A000203(n) / A344695(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

A344696(n) = { my(u=sigma(n)); (u/gcd(u, A001615(n))); };

CROSSREFS

Cf. A000203, A001615, A005117 (positions of ones), A344695, A344697, A344698, A344702.