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A254340
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Sum of the distinct prime factors of n plus n+1: a(n) = A008472(n) + n + 1.
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0
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2, 5, 7, 7, 11, 12, 15, 11, 13, 18, 23, 18, 27, 24, 24, 19, 35, 24, 39, 28, 32, 36, 47, 30, 31, 42, 31, 38, 59, 41, 63, 35, 48, 54, 48, 42, 75, 60, 56, 48, 83, 55, 87, 58, 54, 72, 95, 54, 57, 58, 72, 68, 107, 60, 72, 66, 80, 90, 119, 71, 123, 96, 74, 67, 84
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OFFSET
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1,1
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COMMENTS
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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.
If n is semiprime, then a(n) = sigma(n).
If m and n are coprime, then a(m*n) = a(m) + a(n) + (m-1)*(n-1) - 2. - Robert Israel, May 04 2015
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LINKS
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FORMULA
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MAPLE
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map(t -> t+1+convert(numtheory:-factorset(t), `+`), [$1..100]); # Robert Israel, May 04 2015
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MATHEMATICA
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Table[n + 1 + DivisorSum[n, # &, PrimeQ[#] &], {n, 100}]
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PROG
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(PARI) vector(100, n, vecsum(factor(n)[, 1]~)+n+1) \\ Derek Orr, May 13 2015
(Magma) [&+PrimeDivisors(n)+n+1: n in [1..70]]; // Bruno Berselli, May 27 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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