A346103 Numerators of sequence whose Dirichlet convolution with itself yields A342920.

1, 1, 1, 7, 1, 3, 1, 57, 47, 3, 1, 19, 1, 3, 11, 747, 1, 139, 1, 19, 11, 3, 1, 319, 199, 3, 81, 19, 1, 231, 1, -265, 11, 3, 251, 873, 1, 3, 11, 191, 1, 79, 1, 19, 299, 3, 1, -157, 5943, 595, 11, 19, 1, 151, 187, 31, 11, 3, 1, 269, 1, 3, 507, -957, 527, 31, 1, 19, 11, 223, 1, 18787, 1, 3, 8915, 19, 483, 31, 1, 2147, 19355

Offset: 1

Author

Antti Karttunen, Jul 09 2021

Keywords

• sign
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A046644 (gives the denominators).

Cf. A108951, A324886, A342001, A342002, A342920, A346104.

Programs

PARI

up_to = 2310;
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&dA317937.
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A342920(n) = A342002(A108951(n));
vA346103aux = DirSqrt(vector(up_to, n, A342920(n)));
A346103(n) = numerator(vA346103aux[n]);