A378520 Dirichlet inverse of A336840, where A336840 is the inverse Möbius transform of A048673.

1, -3, -4, 1, -5, 10, -7, -1, -1, 12, -8, -2, -10, 16, 14, -2, -11, 5, -13, -2, 18, 18, -16, 6, -5, 22, -8, -2, -17, -20, -20, -4, 20, 24, 20, 1, -22, 28, 24, 8, -23, -20, -25, -2, 11, 34, -28, 14, -19, 18, 26, -2, -31, 32, 22, 12, 30, 36, -32, 4, -35, 42, 17, -8, 26, -20, -37, -2, 36, -14, -38, 3, -41, 46, 26, -2, 26

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to prime indices in the factorization of n

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A336840(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A323893(d)).

a(n) = A349915(A003961(n)).

Prog

(PARI)
A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A336840(n) = sumdiv(n, d, A048673(d));
memoA378520 = Map();
A378520(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378520, n, &v), v, v = -sumdiv(n, d, if(d<n, A336840(n/d)*A378520(d), 0)); mapput(memoA378520, n, v); (v)));

Crossrefs

Möbius transform of A323893.

Dirichlet inverse of A336840.

Cf. A003961, A008683, A349915.

Sequence in context: A133779 A137911 A019599 * A177971 A114156 A348972

Adjacent sequences: A378517 A378518 A378519 * A378521 A378522 A378523

Keyword

sign,new

Author

Antti Karttunen, Nov 30 2024

Status

approved