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

Author

Gus Wiseman, Jul 26 2019

Keywords

• nonn
• frac

Comments

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

Examples

			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.
		

Crossrefs

Denominators are A326840.

Positions of 1's are A000040.

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

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

Programs

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}]]