A379110 Dirichlet inverse of A324892, where A324892 is multiplicative with a(p^e) = p^e if sigma(p^e) is prime, and 1 otherwise.

1, -2, -1, 0, -1, 2, -1, 7, -8, 2, -1, 0, -1, 2, 1, -28, -1, 16, -1, 0, 1, 2, -1, -7, -24, 2, 16, 0, -1, -2, -1, 59, 1, 2, 1, 0, -1, 2, 1, -7, -1, -2, -1, 0, 8, 2, -1, 28, 0, 48, 1, 0, -1, -32, 1, -7, 1, 2, -1, 0, -1, 2, 8, -75, 1, -2, -1, 0, 1, -2, -1, -56, -1, 2, 24, 0, 1, -2, -1, 28, 56, 2, -1, 0, 1, 2, 1, -7

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..32769

Index entries for sequences related to sigma(n).

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A324892(n/d) * a(d).

Prog

(PARI)
A324892(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i, 1]^isprime(sigma(f[i, 1]^f[i, 2])))^f[i, 2]); };
memoA379110 = Map();
A379110(n) = if(1==n, 1, my(v); if(mapisdefined(memoA379110, n, &v), v, v = -sumdiv(n, d, if(d<n, A324892(n/d)*A379110(d), 0)); mapput(memoA379110, n, v); (v)));

Crossrefs

Cf. A000203, A324892.

Sequence in context: A080941 A346705 A177405 * A378716 A362421 A323302

Adjacent sequences: A379107 A379108 A379109 * A379111 A379112 A379113

Keyword

sign,mult

Author

Antti Karttunen, Dec 17 2024

Status

approved