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A324542
Möbius transform of A324118, where A324118(n) = A000593(A156552(n)).
6
0, 1, 1, 3, 1, 4, 1, 4, 3, 11, 1, 3, 1, 16, 4, 16, 1, 5, 1, 4, 11, 46, 1, 8, 3, 82, 4, 27, 1, 10, 1, 8, 16, 174, 4, 20, 1, 256, 46, 32, 1, 4, 1, 17, 3, 798, 1, 8, 3, 15, 82, 45, 1, 12, 11, 20, 174, 1300, 1, 2, 1, 2734, 4, 72, 16, 27, 1, 125, 256, 8, 1, 20, 1, 4354, 5, 363, 4, 25, 1, 8, 16, 10926, 1, 53, 46, 20518, 798, 168, 1, 35, 11, 317
OFFSET
1,4
COMMENTS
The first three zeros after a(1) occur at n = 192, 288, 3645.
The first negative term is a(150) = -1. There are 184 negative terms among the first 4473 terms.
FORMULA
a(n) = Sum_{d|n} A008683(n/d) * A324118(d).
PROG
(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
A322993(n) = A156552(2*A246277(n));
memoA324118 = Map();
A324118(n) = if(1==n, 0, my(v); if(mapisdefined(memoA324118, n, &v), v, v=sigma(A322993(n)); mapput(memoA324118, n, v); (v)));
A324542(n) = sumdiv(n, d, moebius(n/d)*A324118(d));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Mar 07 2019
STATUS
approved