A362983 Number of prime factors of n (with multiplicity) that are greater than the least.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 1, 0, 1, 0, 2, 1, 1, 1

Offset: 1

Author

Gus Wiseman, May 18 2023

Keywords

• nonn

Examples

			The prime factorization of 360 is 2*2*2*3*3*5, with factors greater than the least 3*3*5, so a(360) = 3.
		

Crossrefs

Positions of 0's are A000961.

Positions of numbers > 0 are A024619.

Positions of first appearances appear to be A099856.

For "less than greatest" instead of "greater than least" we have A325226.

For multiplicities instead of parts we have A363131.

A027746 lists prime factors, A112798 indices, A124010 exponents.

A047966 counts uniform partitions, ranks A072774.

A363128 counts partitions with more than one non-mode, complement A363129.

Cf. A001221, A001222, A052126, A053585, A061395, A064989, A071178, A105441, A307517, A325230.

Programs

Mathematica

Table[PrimeOmega[n]-If[n==1,0,FactorInteger[n][[1,2]]],{n,30}]

Formula

a(n) = A001222(n) - A067029(n).

a(n) = A001222(A028234(n)).