A104414 Number of prime factors, with multiplicity, of the heptanacci numbers A066178.

0, 0, 1, 2, 3, 4, 5, 6, 1, 2, 6, 3, 7, 6, 9, 8, 1, 4, 2, 5, 6, 5, 8, 9, 2, 3, 10, 6, 7, 7, 16, 10, 4, 2, 7, 5, 6, 9, 12, 10, 4, 3, 6, 4, 9, 8, 14, 12, 2, 3, 7, 6, 11, 8, 7, 10, 5, 5, 12, 6, 7, 9, 12, 11, 3, 4, 3, 6, 7, 5, 6, 11, 4, 2, 9, 4, 7, 9, 14, 8, 4, 3

Offset: 0

Author

Jonathan Vos Post, Mar 06 2005

Keywords

• easy
• nonn

Comments

Prime heptanacci numbers: a(2) = 2, a(8) = 127, a(16) = 31489, ... Semiprime heptanacci numbers: a(4) = 4 = 2^2, a(9) = 253 = 11 * 23, a(18) = 124946 = 2 * 62473, a(24) = 7805695 = 5 * 1561139.

Examples

			a(0)=a(1)=0 because the first two nonzero heptanacci numbers are both 1, which has zero prime divisors.
a(2)=1 because the 3rd nonzero heptanacci number is 2, a prime, with only one prime divisor.
a(3)=2 because the 4th nonzero pentanacci number is 4 = 2^2 which has (with multiplicity) 2 prime divisors (which happen to be equal).
a(4)=3 because the 5th nonzero heptanacci number is 8 = 2^3.
a(12)= 7 because A066178(12) = 2000 = 2^4 * 5^3 which has seven prime factors (four of the 2, three of them 5).
		

Crossrefs

Cf. A001222, A066178, A104411, A104412, A104413.

Programs

Mathematica

PrimeOmega[#]&/@LinearRecurrence[{1,1,1,1,1,1,1},{1,1,2,4,8,16,32},100] (* Harvey P. Dale, Oct 08 2015 *)

Formula

a(n) = A001222(A066178(n)). a(n) = bigomega(A066178(n)).

Extensions

More terms from Harvey P. Dale, Oct 08 2015