

A075255


a(n) = n  (sum of primes factors of n (with repetition)).


9



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
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OFFSET

1,8


LINKS

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


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


CROSSREFS

Cf. A001414, A008472, A075254, A075653.
Cf. A145834 (= 0 followed by the nonzero terms of this sequence).  M. F. Hasler, Oct 31 2008
Sequence in context: A127572 A021815 A238525 * A135498 A104172 A091408
Adjacent sequences: A075252 A075253 A075254 * A075256 A075257 A075258


KEYWORD

nonn


AUTHOR

Zak Seidov, Sep 10 2002


STATUS

approved



