A329037 a(n) = Product_{d|n, d>1} A008578(1+A286561(A276086(n),d)), where A286561(x,d) gives the exponent of the highest power of d dividing x.

1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 12, 1, 1, 1, 1, 5, 2, 1, 1, 1, 21, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 12, 1, 1, 1, 2, 10, 2, 1, 1, 1, 7, 2, 2, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 12, 1, 1, 1, 1, 48, 1, 3, 1, 1, 5, 2, 1, 1, 3, 7, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 10, 2, 2, 1, 1, 1, 1, 720

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base

Formula

a(n) = Product_{d|n, d>1} A008578(1+A286561(A276086(n),d)).

1+A001222(a(n)) = A327168(n).

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329037(n) = { my(m=1, x=A276086(n), v); fordiv(n, d, if((d>1) && ((v = valuation(x, d))>0), m *= prime(v))); (m); };

Crossrefs

Cf. A008578, A276086, A286561, A327168.

Cf. also A327167.

Sequence in context: A324119 A083382 A327168 * A279794 A025900 A118383

Adjacent sequences: A329034 A329035 A329036 * A329038 A329039 A329040

Keyword

nonn

Author

Antti Karttunen, Nov 08 2019

Status

approved