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A347117
Möbius transform of A329603.
4
2, 3, 6, 10, 16, 0, 48, 30, 12, 104, 96, 12, 240, 192, 8, 90, 336, 54, 576, 240, 16, 504, 720, 36, 24, 600, 40, 480, 1056, -122, 1680, 270, 96, 1104, 96, 132, 1920, 1224, 144, 720, 2736, 1064, 3360, 1200, 0, 1920, 3696, 108, 60, 126, 624, 1680, 4416, 422, 336, 1440, 768, 3144, 5616, -228, 6960, 3120, 416, 810, 624
OFFSET
1,1
FORMULA
a(n) = Sum_{d|n} A008683(n/d) * A329603(d).
PROG
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A329603(n) = A005940(2+(3*A156552(n)));
A347117(n) = sumdiv(n, d, moebius(n/d)*A329603(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Aug 21 2021
STATUS
approved