A387879 Number of prime factors with multiplicity (bigomega) of the least common multiple of the prime indices of n.

0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 1, 3, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 0, 2, 1, 3, 1, 3, 3, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 0, 2, 2, 1, 1, 3, 3, 3, 1, 2, 3, 2, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2

Offset

1,7

Comments

Warning: Do not confuse with the GCD version A387579.

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=1..87.

Formula

a(n) = A001222(A290103(n)).

Example

The prime indices of 2257 are {12,18}, with least common multiple 36, with prime factors {2,2,3,3}, so a(2257) = 4.

Mathematica

Table[If[n==1, 0, PrimeOmega[LCM@@PrimePi/@First/@FactorInteger[n]]], {n, 100}]

Crossrefs

Positions of 0 are A000079.

Positions of first appearances appear to be A033844, see also A062447.

For product instead of LCM we have A302242.

Positions of terms < 2 are A302594.

For distinct prime factors (omega) we have A303975, for GCD A387135.

Positions of 1 are A371127.

For GCD instead of LCM we have A387579.

A000005 counts divisors.

A001222 counts prime factors, distinct A001221.

A001414 adds up distinct prime divisors.

A003963 multiplies together prime indices.

A112798 lists prime indices, row sums A056239 or A066328.

A120383 lists numbers divisible by all of their prime indices.

A289508 gives greatest common divisor of prime indices.

Cf. A000720, A055396, A061395, A289509, A318978, A335433, A335448, A355731, A355733, A355737, A355740, A370820, A387114.

Sequence in context: A369258 A337930 A340691 * A216658 A214020 A029425

Adjacent sequences: A387876 A387877 A387878 * A387880 A387881 A387882

Keyword

nonn

Author

Gus Wiseman, Sep 11 2025

Status

approved