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

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.

Cf. also A344756.

Sequence in context: A348048 A348985 A348504 * A336457 A271498 A365332

Adjacent sequences: A344693 A344694 A344695 * A344697 A344698 A344699

Keyword

nonn

Author

Antti Karttunen, May 26 2021

Status

approved