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

1,4

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

Prog

(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&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
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]);

Crossrefs

Cf. A046644 (gives the denominators).

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

Sequence in context: A340144 A340141 A342377 * A039616 A344967 A362923

Adjacent sequences: A346100 A346101 A346102 * A346104 A346105 A346106

Keyword

sign,frac

Author

Antti Karttunen, Jul 09 2021

Status

approved