A293515 a(n) = Product_{d^k|n, d>1, k>1} prime(A286561(n,d)-1), where A286561(n,d) gives the highest exponent of d dividing n.

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 10, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 14, 1, 1, 1, 8, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 10, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 66, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 2, 2, 1, 1, 1, 10, 10, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 14, 1, 2, 2, 8, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 1, 10, 1, 1, 1, 2, 2

Offset: 1

Author

Antti Karttunen, Nov 11 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000040, A008578, A286561.

Cf. A293514, A294875.

Cf. A046951.

Programs

PARI

A293515(n) = { my(m=1,v); fordiv(n,d,if(d>1, v = valuation(n,d); if(v>1, m *= prime(v-1)))); m; };

Formula

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

a(n) = A064989(A293514(n)).

Other identities. For all n >= 1:

1 + A001222(a(n)) = A046951(n).