A075254 a(n) = n + (sum of prime factors of n taken with repetition).

1, 4, 6, 8, 10, 11, 14, 14, 15, 17, 22, 19, 26, 23, 23, 24, 34, 26, 38, 29, 31, 35, 46, 33, 35, 41, 36, 39, 58, 40, 62, 42, 47, 53, 47, 46, 74, 59, 55, 51, 82, 54, 86, 59, 56, 71, 94, 59, 63, 62, 71, 69, 106, 65, 71, 69, 79, 89, 118, 72, 122, 95, 76, 76, 83, 82, 134, 89, 95, 84, 142

Offset

1,2

Comments

a(n) = n + A001414(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

a(6)=11 because 6=2*3, sopfr(6)=2+3=5 and 6+5=11.

Maple

A075254 := proc(n)
    n+A001414(n) ;
end proc: # R. J. Mathar, Jul 27 2015

Mathematica

Table[If[n==1, 1, n +Plus@@Times@@@FactorInteger@n], {n, 80}] (* G. C. Greubel, Jan 10 2019 *)

Prog

(Haskell)
a075254 n = n + a001414 n  -- Reinhard Zumkeller, Feb 27 2012
(PARI) a(n) = my(f = factor(n)); n += sum(k=1, #f~, f[k, 1]*f[k, 2]); \\ Michel Marcus, Feb 22 2017
(Magma) [n eq 1 select 1 else (&+[p[1]*p[2]: p in Factorization(n)]) + n: n in [1..80]]; // G. C. Greubel, Jan 10 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 10 2019

Crossrefs

Cf. A001414, A008472, A075255.

Cf. A096461 (iteration).

Sequence in context: A349707 A272475 A184016 * A284913 A139203 A179372

Adjacent sequences: A075251 A075252 A075253 * A075255 A075256 A075257

Keyword

nonn

Author

Zak Seidov, Sep 10 2002

Status

approved