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A359164
Difference between Kimberling's paraphrases and its Möbius transform.
2
0, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 4, 4, 1, 1, 5, 1, 3, 5, 6, 1, 2, 3, 7, 5, 4, 1, 8, 1, 1, 7, 9, 6, 5, 1, 10, 8, 3, 1, 11, 1, 6, 11, 12, 1, 2, 4, 13, 10, 7, 1, 14, 8, 4, 11, 15, 1, 8, 1, 16, 14, 1, 9, 17, 1, 9, 13, 18, 1, 5, 1, 19, 18, 10, 9, 20, 1, 3, 14, 21, 1, 11, 11, 22, 16, 6, 1, 23, 10, 12, 17, 24, 12
OFFSET
1,6
FORMULA
a(n) = A003602(n) - A349136(n).
a(n) = Sum_{d|n, d<n} A349136(d).
a(n) = -Sum_{d|n, d<n} A008683(n/d)*A003602(d).
a((2^e)*prime(n)) = A111333(n) for all n >= 1 and e >= 1.
PROG
(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A349136(n) = sumdiv(n, d, moebius(d)*A003602(n/d));
A359164(n) = (A003602(n) - A349136(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 22 2022
STATUS
approved