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URL: https://oeis.org/A075255

⇱ A075255 - OEIS

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A075255
a(n) = n - (sum of prime factors of n (with repetition)).
42
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
1,8
LINKS
FORMULA
a(n) = n - A001414(n).
a(n) = 0 if n is prime or if n = 4. - Alonso del Arte, Jul 31 2018
EXAMPLE
a(6) = 1 because 6 = 2 * 3, sopfr(6) = 2 + 3 = 5 and 6 - 5 = 1.
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 *)
PROG
(PARI) A075255(n)=n-sum(i=1, #n=factor(n)~, n[1, i]*n[2, i]) \\ M. F. Hasler, Oct 31 2008
(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
(SageMath) [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
(Python)
from sympy import factorint
def A075255(n): return n - sum(factorint(n, multiple=True)) # Chai Wah Wu, May 19 2022
CROSSREFS
Cf. A145834 (= 0 followed by the nonzero terms of this sequence). - M. F. Hasler, Oct 31 2008
Sequence in context: A021815 A238525 A359788 * A135498 A104172 A091408
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 10 2002
STATUS
approved