A075255 a(n) = n - (sum of prime factors of n (with repetition)).

1, 0, 0, 0, 0, 1, 0, 2, 3, 3, 0, 5, 0, 5, 7, 8, 0, 10, 0, 11, 11, 9, 0, 15, 15, 11, 18, 17, 0, 20, 0, 22, 19, 15, 23, 26, 0, 17, 23, 29, 0, 30, 0, 29, 34, 21, 0, 37, 35, 38, 31, 35, 0, 43, 39, 43, 35, 27, 0, 48, 0, 29, 50, 52, 47, 50, 0, 47, 43, 56, 0, 60, 0, 35, 62, 53, 59, 60

Offset: 1

Author

Zak Seidov, Sep 10 2002

Keywords

• nonn

Examples

			a(6) = 1 because 6 = 2 * 3, sopfr(6) = 2 + 3 = 5 and 6 - 5 = 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A008472, A075254, A075653.

Cf. A145834 (= 0 followed by the nonzero terms of this sequence). - M. F. Hasler, Oct 31 2008

Programs

Magma

[n eq 1 select 1 else n-(&+[p[1]*p[2]: p in Factorization(n)]): n in [1..80]]; // G. C. Greubel, Jan 11 2019

Maple

a:= n-> n-add(i[1]*i[2], i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 07 2015

Mathematica

Join[{1}, Table[n - Total[Times@@@FactorInteger[n]], {n, 2, 80}]] (* Harvey P. Dale, Sep 20 2011 *)

PARI

A075255(n)=n-sum(i=1,#n=factor(n)~,n[1,i]*n[2,i]) \\ M. F. Hasler, Oct 31 2008

Python

from sympy import factorint
def A075255(n): return n - sum(factorint(n,multiple=True)) # Chai Wah Wu, May 19 2022

Sage

[n - sum(factor(n)[j][0]*factor(n)[j][1] for j in range(0, len(factor(n)))) for n in range(1, 80)] # G. C. Greubel, Jan 11 2019

Formula

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

a(n) = 0 if n is prime or if n = 4. - Alonso del Arte, Jul 31 2018