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%I #29 Sep 08 2022 08:46:11
%S 2,5,7,7,11,12,15,11,13,18,23,18,27,24,24,19,35,24,39,28,32,36,47,30,
%T 31,42,31,38,59,41,63,35,48,54,48,42,75,60,56,48,83,55,87,58,54,72,95,
%U 54,57,58,72,68,107,60,72,66,80,90,119,71,123,96,74,67,84
%N Sum of the distinct prime factors of n plus n+1: a(n) = A008472(n) + n + 1.
%C If n is prime, then a(n) = 2n+1; thus if n is a Sophie Germain prime p, then a(p) gives the safe prime q=2p+1.
%C If n is semiprime, then a(n) = sigma(n).
%C If m and n are coprime, then a(m*n) = a(m) + a(n) + (m-1)*(n-1) - 2. - _Robert Israel_, May 04 2015
%F a(n) = A075653(n) + 1 = A074372(n) + n. [_Bruno Berselli_, May 27 2015]
%p map(t -> t+1+convert(numtheory:-factorset(t),`+`),[$1..100]); # _Robert Israel_, May 04 2015
%t Table[n + 1 + DivisorSum[n, # &, PrimeQ[#] &], {n, 100}]
%o (PARI) vector(100,n,vecsum(factor(n)[,1]~)+n+1) \\ _Derek Orr_, May 13 2015
%o (Magma) [&+PrimeDivisors(n)+n+1: n in [1..70]]; // _Bruno Berselli_, May 27 2015
%Y Cf. A000203 (sigma), A008472 (sopf), A074372, A075653.
%Y Cf. A005384 (Sophie Germain primes), A005385 (safe primes).
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, May 03 2015
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