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

0,4

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.

Links

Table of n, a(n) for n=0..81.

Formula

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

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A338495 A053828 A033927 * A279049 A337223 A125934

Adjacent sequences: A104411 A104412 A104413 * A104415 A104416 A104417

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 06 2005

Extensions

More terms from Harvey P. Dale, Oct 08 2015

Status

approved