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A347957 Dirichlet convolution of A001221 (omega) with A003602 (Kimberling's paraphrases). 5
0, 1, 1, 2, 1, 5, 1, 3, 3, 6, 1, 9, 1, 7, 7, 4, 1, 14, 1, 11, 8, 9, 1, 13, 4, 10, 8, 13, 1, 28, 1, 5, 10, 12, 9, 25, 1, 13, 11, 16, 1, 34, 1, 17, 22, 15, 1, 17, 5, 25, 13, 19, 1, 38, 11, 19, 14, 18, 1, 49, 1, 19, 26, 6, 12, 46, 1, 23, 16, 44, 1, 36, 1, 22, 31, 25, 12, 52, 1, 21, 22, 24, 1, 60, 14, 25, 19, 25, 1, 86 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Jon Maiga, Computer-generated formulas for A347957, Sequence Machine.
FORMULA
a(n) = Sum_{d|n} A001221(n/d) * A003602(d).
From Antti Karttunen, Nov 13 2021: (Start)
The following two convolutions were found by Jon Maiga's Sequence Machine search algorithm. The first one is obvious, and even the second one should not be too hard to prove:
a(n) = Sum_{d|n} A023900(n/d) * A347956(d).
a(n) = Sum_{d|n} A181988(n/d) * A205745(d).
(End)
PROG
(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A347957(n) = sumdiv(n, d, omega(n/d)*A003602(d));
CROSSREFS
Sequence in context: A332085 A055205 A342001 * A369038 A161686 A289621
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 20 2021
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)