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A344696 a(n) = sigma(n) / gcd(sigma(n), A001615(n)). 9
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2021
STATUS
approved

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Last modified June 23 18:37 EDT 2024. Contains 373653 sequences. (Running on oeis4.)