A113901 Product of omega(n) and bigomega(n) = A001221(n)*A001222(n), where omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.

0, 1, 1, 2, 1, 4, 1, 3, 2, 4, 1, 6, 1, 4, 4, 4, 1, 6, 1, 6, 4, 4, 1, 8, 2, 4, 3, 6, 1, 9, 1, 5, 4, 4, 4, 8, 1, 4, 4, 8, 1, 9, 1, 6, 6, 4, 1, 10, 2, 6, 4, 6, 1, 8, 4, 8, 4, 4, 1, 12, 1, 4, 6, 6, 4, 9, 1, 6, 4, 9, 1, 10, 1, 4, 6, 6, 4, 9, 1, 10, 4, 4, 1, 12, 4, 4, 4, 8, 1, 12, 4, 6, 4, 4, 4, 12, 1, 6, 6, 8, 1, 9

Offset

1,4

Comments

a(n) = 1 iff n is prime.

A068993(a(n)) = 4. - Reinhard Zumkeller, Mar 13 2011

Positions of first appearances are A328964. - Gus Wiseman, Nov 05 2019

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

Table[PrimeNu[n]*PrimeOmega[n], {n, 1, 50}] (* G. C. Greubel, Apr 23 2017 *)

Prog

(PARI) list(n) = { local(x); for(x=1, n, print1(omega(x)*bigomega(x)", ") ) }

Crossrefs

A307409(n) is (bigomega(n) - 1) * omega(n).

A328958(n) is sigma_0(n) - bigomega(n) * omega(n).

Cf. A000005, A001221, A001222, A060687, A070175, A071625, A124010, A303555, A320632, A323023, A328956, A328957, A328964, A328965.

Sequence in context: A067614 A341308 A353359 * A062799 A063647 A353379

Adjacent sequences: A113898 A113899 A113900 * A113902 A113903 A113904

Keyword

easy,nonn

Author

Cino Hilliard, Jan 29 2006

Status

approved