A104418 Number of prime factors, with multiplicity, of the nonzero 9-acci numbers.

0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 6, 3, 5, 7, 9, 9, 11, 9, 3, 2, 2, 8, 7, 7, 7, 10, 11, 10, 3, 2, 7, 8, 11, 7, 12, 13, 15, 11, 3, 2, 6, 7, 7, 10, 9, 12, 12, 13, 5, 2, 5, 8, 8, 7, 13, 12, 10, 12, 6, 3, 3, 6, 12, 11, 12, 10, 12, 12, 2, 6, 12, 8, 11, 9, 14, 13, 13, 13, 7, 2

Offset

1,4

Comments

Prime 9-acci numbers: b(3) = 2, b(12) = 1021, ... Semiprime 9-acci numbers: b(4) = 4 = 2^2, b(11) = 511 = 7 * 73, b(22) = 1035269 = 47 * 22027, b(23) = 2068498 = 2 * 1034249, b(32) = 1049716729 = 1051 * 998779 b(42) = 1064366053385 = 5 * 212873210677, b(52) = 1079219816432629 = 28669 * 37644138841, b(71) = 555323195719171835391 = 3 * 185107731906390611797, b(82) = 1125036467745713090813969 = 37 * 30406391020154407859837.

Links

Table of n, a(n) for n=1..82.

Formula

a(n) = A001222(A104144(n+7)).

Example

a(1)=a(2)=0 because the first two nonzero 9-acci numbers are both 1, which has zero prime divisors.
a(3)=1 because the 3rd nonzero 9-acci number is 2, a prime, with only one prime divisor.
a(4)=2 because the 4th nonzero 9-acci number is 4 = 2^2 which has (with multiplicity) 2 prime divisors (which happen to be equal).
a(5)=3 because the 5th nonzero 9-acci number is 8 = 2^3.
a(13) = 6 because b(13) = 2040 = 2^3 * 3 * 5 * 17 so has 6 prime factors (2 with multiplicity 3 and 3, 5 and 17 once each).

Crossrefs

Cf. A001222, A104411, A104412, A104413, A104414, A104415.

Sequence in context: A080465 A347689 A151950 * A173528 A245345 A043268

Adjacent sequences: A104415 A104416 A104417 * A104419 A104420 A104421

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 06 2005

Status

approved