A068318 Sum of prime factors of n-th semiprime.

4, 5, 6, 7, 9, 8, 10, 13, 10, 15, 14, 19, 12, 21, 16, 25, 14, 20, 16, 22, 31, 33, 18, 26, 39, 18, 43, 22, 45, 32, 20, 34, 49, 24, 55, 40, 28, 61, 24, 22, 63, 44, 46, 26, 69, 50, 73, 24, 34, 75, 36, 81, 56, 30, 85, 26, 62, 91, 64, 42, 28, 99, 70, 103, 36, 46, 105, 30, 74, 109

Offset

1,1

Comments

a(n) = A003415(A001358(n)), the arithmetic derivative.

Odd k is a term if and only if k - 2 is prime. Goldbach's conjecture implies that every even number k >= 4 is a term. - Jianing Song, May 26 2021

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Robert G. Wilson v, Graph of n and a(n)

Formula

a(n) = A001414(A001358(n)).

If A001358(n)=s*p, then in this sequence a(n)=s+p.

a(n) = A084126(n)+A084127(n). - Reinhard Zumkeller, Jul 24 2006 [Typo in formula fixed by Zak Seidov, Aug 23 2014 ]

Example

a(2)=5 because A001358(2)=6=2*3 and 2+3=5.

Maple

with(numtheory): a:=proc(n) if bigomega(n)=2 and nops(factorset(n))=2 then factorset(n)[1]+factorset(n)[2] elif bigomega(n)=2 then 2*sqrt(n) else fi end: seq(a(n), n=1..214); # Emeric Deutsch

Mathematica

f[n_] := Total[#1*#2 & @@@ FactorInteger@ n]; f@# & /@ Select[Range@300, PrimeOmega@# == 2 &] (* Robert G. Wilson v, Jan 23 2013 *)

Crossrefs

Semiprimes are in A001358.

Cf. A120831, A120832, A120833, A120834, A109313.

Sequence in context: A143789 A068521 A196697 * A347932 A242337 A201739

Adjacent sequences: A068315 A068316 A068317 * A068319 A068320 A068321

Keyword

nonn

Author

Reinhard Zumkeller, Feb 27 2002

Status

approved