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A340365
a(n) = A005940(n) / gcd(A005940(n), A324106(n)), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).
4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 13, 1, 11, 1, 1, 1, 21, 1, 1, 35, 1, 1, 5, 1, 1, 1, 1, 1, 49, 1, 1, 1, 3, 1, 49, 1, 1, 9, 1, 1, 27, 1, 17, 13, 1, 1, 13, 11, 1, 1, 1, 1, 55, 1, 55, 21, 1, 1, 1, 1, 1, 35, 7, 1, 21, 1, 1, 5, 7, 1, 875, 1, 27, 1, 1, 1, 121
OFFSET
1,15
COMMENTS
It is conjectured that A070776 gives the positions of all ones after the initial one. If that holds, then for all i, j: a(i) = a(j) => A340363(i) = A340363(j).
LINKS
FORMULA
a(n) = A005940(n) / A340364(n) = A005940(n) / gcd(A005940(n), A324106(n)).
PROG
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i, 1]^f[i, 2])); };
A340365(n) = { my(t=A005940(n)); t / gcd(t, A324106(n)); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 06 2021
STATUS
approved