A326839 Numerator of A056239(n)/A061395(n) where A056239 is sum of prime indices and A061395 is maximum prime index.

0, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 2, 1, 5, 5, 4, 1, 5, 1, 5, 3, 6, 1, 5, 2, 7, 3, 3, 1, 2, 1, 5, 7, 8, 7, 3, 1, 9, 4, 2, 1, 7, 1, 7, 7, 10, 1, 3, 2, 7, 9, 4, 1, 7, 8, 7, 5, 11, 1, 7, 1, 12, 2, 6, 3, 8, 1, 9, 11, 2, 1, 7, 1, 13, 8, 5, 9, 3, 1, 7, 4, 14, 1, 2, 10

Offset

1,4

Comments

This is a dual form of the average of an integer partition specified by its Heinz number: A326567/A326568.

Links

Table of n, a(n) for n=1..85.

Example

The sequence of fractions begins: 0, 1, 1, 2, 1, 3/2, 1, 3, 2, 4/3, 1, 2, 1, 5/4, 5/3, 4, 1, 5/2, 1, 5/3.

Mathematica

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

Crossrefs

Denominators are A326840.

Positions of 1's are A000040.

Cf. A001222, A047993, A056239, A061395, A112798, A316413.

Cf. A326567/A326568, A326836, A326845, A326848, A326850.

Sequence in context: A029231 A025808 A144079 * A071575 A307908 A366737

Adjacent sequences: A326836 A326837 A326838 * A326840 A326841 A326842

Keyword

nonn,frac

Author

Gus Wiseman, Jul 26 2019

Status

approved