A290104 a(n) = A003963(n) / A290103(n).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 2, 3, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 1

Offset

1,9

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). Then a(n) is the product divided by the LCM of the integer partition with Heinz number n. - Gus Wiseman, Aug 01 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A003963(n) / A290103(n).

Other identities. For all n >= 1:

a(A181819(n)) = A005361(n)/A072411(n).

Example

n = 21 = 3 * 7 = prime(2) * prime(4), thus A003963(21) = 2*4 = 8, while A290103(21) = lcm(2,4) = 4, so a(21) = 8/4 = 2.

Mathematica

Table[If[n == 1, 1, Apply[Times, Map[PrimePi[#1]^#2 & @@ # &, #]] / Apply[LCM, PrimePi[#[[All, 1]] ]]] &@ FactorInteger@ n, {n, 120}] (* Michael De Vlieger, Aug 14 2017 *)

Prog

(Scheme) (define (A290104 n) (/ (A003963 n) (A290103 n)))

Crossrefs

Differs from A290106 for the first time at n=21.

Cf. A003963, A056239, A074761, A289509, A290103, A290105, A296150, A316429, A316431.

Sequence in context: A060128 A330751 A327407 * A308479 A031280 A134870

Adjacent sequences: A290101 A290102 A290103 * A290105 A290106 A290107

Keyword

nonn

Author

Antti Karttunen, Aug 13 2017

Status

approved