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

1,4

Links

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

Index entries for sequences computed from exponents in factorization of n

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).

Prog

(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; };

Crossrefs

Cf. A000040, A008578, A286561.

Cf. A293514, A294875.

Cf. A046951.

Sequence in context: A321271 A305193 A038538 * A326622 A292777 A088529

Adjacent sequences: A293512 A293513 A293514 * A293516 A293517 A293518

Keyword

nonn

Author

Antti Karttunen, Nov 11 2017

Status

approved