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

1,18

Links

Chris R. Rehmann, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

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.

Mathematica

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

Prog

(PARI) A362983(n) = my(f = factor(n)); sum(k = 2, matsize(f)[1], f[k, 2]); \\ Chris R. Rehmann, Jun 11 2026

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

Sequence in context: A275949 A357924 A351563 * A352822 A090418 A363877

Adjacent sequences: A362980 A362981 A362982 * A362984 A362985 A362986

Keyword

nonn,changed

Author

Gus Wiseman, May 18 2023

Status

approved