A326153 Numerator of the product of prime indices of n divided by the sum of prime indices of n, n > 1.

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 4, 6, 1, 1, 4, 1, 3, 4, 5, 1, 2, 3, 6, 4, 2, 1, 1, 1, 1, 10, 7, 12, 2, 1, 8, 3, 1, 1, 8, 1, 5, 12, 9, 1, 1, 2, 9, 14, 3, 1, 8, 15, 4, 8, 10, 1, 6, 1, 11, 2, 1, 2, 5, 1, 7, 18, 3, 1, 4, 1, 12, 9, 4, 20, 4, 1, 3, 2, 13, 1, 1

Offset

2,5

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=2..84.

Example

The sequence A326153/A326154 begins: 1, 1, 1/2, 1, 2/3, 1, 1/3, 1, 3/4, 1, 1/2, 1, 4/5, 6/5, 1/4, 1, 4/5, 1, 3/5, 4/3, 5/6, 1, 2/5, 3/2, 6/7, 4/3.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Numerator[Times@@primeMS[n]/Plus@@primeMS[n]], {n, 2, 100}]

Crossrefs

Numerator of A003963(n)/A056239(n).

Positions of ones are A326155 without the first term.

Cf. A057567, A057568, A112798, A301987, A325037, A325042, A325044, A326149, A326150, A326151, A326154, A326156, A326158.

Sequence in context: A347049 A054576 A326840 * A199515 A316695 A316767

Adjacent sequences: A326150 A326151 A326152 * A326154 A326155 A326156

Keyword

nonn,frac

Author

Gus Wiseman, Jun 09 2019

Status

approved