A145834 a(n) = difference between the n-th composite number and the sum of its prime factors with repetition.

0, 1, 2, 3, 3, 5, 5, 7, 8, 10, 11, 11, 9, 15, 15, 11, 18, 17, 20, 22, 19, 15, 23, 26, 17, 23, 29, 30, 29, 34, 21, 37, 35, 38, 31, 35, 43, 39, 43, 35, 27, 48, 29, 50, 52, 47, 50, 47, 43, 56, 60, 35, 62, 53, 59, 60, 67, 69, 39, 70, 63, 41, 55, 71, 77, 71, 65, 59, 45, 71, 83, 82, 82

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2500

Formula

a(n) = A075255(A002808(n)) = A002808(n) - A001414(A002808(n)).

Example

a(1) = 4 - (2+2) = 0; a(2) = 6 - (2+3) = 1; a(3) = 8 - (2+2+2) = 2 ; a(4) = 9 - (3+3) = 3; a(5) = 10 - (2+5) = 3.

Mathematica

cnpf[n_]:=n-Total[Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]]; cnpf/@ Select[Range[100], CompositeQ] (* Harvey P. Dale, Aug 31 2021 *)

Prog

(PARI) A145834(n)={for(k=0, primepi(n), isprime(n++)&k--); n+0-sum(i=1, #n=factor(n)~, n[1, i]*n[2, i])} \\ M. F. Hasler, Oct 31 2008

Crossrefs

Cf. A001414, A002808, A075255.

Sequence in context: A363433 A210336 A280271 * A339246 A341142 A130006

Adjacent sequences: A145831 A145832 A145833 * A145835 A145836 A145837

Keyword

nonn

Author

Alexander R. Povolotsky, Oct 20 2008

Extensions

Edited and extended by Ray Chandler, Oct 24 2008

Status

approved