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A377874
Parity of A083345(n), where A083345(n) = n' / gcd(n,n') = numerator of Sum(e/p: n=Product(p^e)).
8
0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0
OFFSET
1
COMMENTS
This is one's complement of A369001. See more comments and formulas in that sequence.
FORMULA
a(n) = A000035(A083345(n))
a(n) = A166486(A276085(n)).
a(n) = 1 - A369001(n).
For all n >= 1, a(n) >= A165560(n), a(n) >= A377868(n).
EXAMPLE
A083345(174) = 151, therefore a(174) = 1. Note also that A276085(174) = 223092873 is not a multiple of 4.
PROG
(PARI) A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };
CROSSREFS
Parity of A083345. One's complement of A369001.
Characteristic function of A369003, whose complement A369002 gives the positions of 0's.
Cf. A000035, A165560, A166486, A276085, A369980 (run lengths).
Differs from A377868 at the positions given by A377875.
Sequence in context: A334812 A079421 A377868 * A374128 A304438 A168181
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Nov 11 2024
STATUS
approved