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 A344767 Möbius transform of A011772. 3
 1, 2, 1, 4, 3, -1, 5, 8, 6, -2, 9, 1, 11, -1, 0, 16, 15, -1, 17, 7, -1, -1, 21, -1, 20, -2, 18, -4, 27, 11, 29, 32, 0, -2, 5, -5, 35, -1, -1, -8, 39, 14, 41, 17, -2, -1, 45, 1, 42, 0, 0, 23, 51, 1, -3, 33, -1, -2, 57, -12, 59, -1, 15, 64, 10, 0, 65, -4, 0, 7, 69, 48, 71, -2, -1, 33, 6, 1, 77, 33, 54, -2, 81, 27, 15, -1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = Sum_{d|n} A008683(n/d) * A011772(d). PROG (PARI) A344767(n) = sumdiv(n, d, moebius(n/d)*A011772(d)); (Python 3.8+) from itertools import combinations from math import prod from sympy import factorint, divisors from sympy.ntheory.modular import crt from sympy.ntheory import mobius def A011772(n):     plist = [p**q for p, q in factorint(2*n).items()]     return 2*n-1 if len(plist) == 1 else min(min(crt([m, 2*n//m], [0, -1])[0], crt([2*n//m, m], [0, -1])[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))) def A344767(n): return sum(mobius(n//d)*A011772(d) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 20 2021 CROSSREFS Cf. A008683, A011772, A344768. Sequence in context: A332332 A335259 A093682 * A187883 A134543 A305540 Adjacent sequences:  A344764 A344765 A344766 * A344768 A344769 A344770 KEYWORD sign,look AUTHOR Antti Karttunen, May 30 2021 STATUS approved

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)