A135592 a(1)=1; for n > 1, a(n) is number of earlier terms equal to number of prime divisors of n.

1, 1, 2, 2, 2, 3, 2, 2, 2, 6, 2, 7, 2, 8, 8, 2, 2, 10, 2, 11, 11, 11, 2, 12, 2, 13, 2, 14, 2, 1, 3, 3, 15, 15, 15, 15, 3, 15, 15, 15, 3, 5, 3, 15, 15, 15, 3, 15, 3, 15, 15, 15, 3, 15, 15, 15, 15, 15, 3, 10, 3, 15, 15, 3, 15, 12, 3, 15, 15, 13, 3, 15, 3, 15, 15, 15, 15, 15, 3, 15, 3, 15, 3, 18

Offset

1,3

Comments

Similar to A125087, but instead of exponents, we use number of prime divisors.

Links

Katarzyna Matylla, Table of n, a(n) for n = 1..1000

Example

a(12)=7 because 12 has 2 prime divisors (2 and 3) and there are 7 2's in a(1), a(2), ..., a(11).

Mathematica

s={1}; Do[AppendTo[s, Count[s, PrimeNu[n]]], {n, 2, 84}]; s (* James C. McMahon, Apr 16 2025 *)

Prog

(Maxima) max:1000; f:makelist(0, i, 1, max); apr:makelist(0, i, 1, max); f[1]:1; apr[2]:1; print(1, 1); for n:2 thru max do block(f[n]:apr[length(ifactors(n))+1], apr[f[n]+1]:apr[f[n]+1]+1);

Crossrefs

Cf. A001221, A125087, A135591.

Sequence in context: A352541 A359438 A279408 * A022912 A318955 A173883

Adjacent sequences: A135589 A135590 A135591 * A135593 A135594 A135595

Keyword

nonn

Author

Katarzyna Matylla, Feb 25 2008

Status

approved