A387579 Number of not necessarily distinct prime factors (bigomega) of the greatest common divisor of the prime indices of n.

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

Offset

1,7

Comments

Warning: Do not confuse with the LCM version A387879.

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(A289508(n)).

Example

The prime indices of 13439 are {24,36}, with greatest common divisor 12, with prime indices {1,1,2}, so a(13439) = 3.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, PrimeOmega[GCD@@prix[n]]], {n, 100}]

Crossrefs

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

Positions of 0 are A289509, complement A318978.

For all divisors instead of just prime factors we have A387114.

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

For LCM (or product) instead of GCD we have A387879.

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, A335433, A335448, A355731, A355733, A355737, A355740, A370820, A387119.

Sequence in context: A309938 A140581 A137277 * A039975 A358679 A016253

Adjacent sequences: A387576 A387577 A387578 * A387580 A387581 A387582

Keyword

nonn

Author

Gus Wiseman, Sep 11 2025

Status

approved