A140611 - OEIS

%I #6 Apr 22 2020 14:44:04

%S 4,6,10,15,16,24,26,32,42,72,78,81,102,111,124,168,172,182,196,205,

%T 209,212,240,243,276,299,301,308,320,326,345,357,361,412,425,426,427,

%U 429,455,477,490,494,526,564,591,605,610,637,638,645,664,670,672,682,684

%N Consecutive N at which the prime running totals of prime factors in composites are found.

%H Harvey P. Dale, <a href="/A140611/b140611.txt">Table of n, a(n) for n = 1..1000</a>

%F Compute prime factors (without multiplicity) of consecutive composite N. Maintain a running sum of these prime factors. Whenever the running total at N is prime, add to the sequence.

%e a(2)=6 because when N=6 the sum of composite prime factors is 7 and this total is prime (nonprime totals are not in this sequence). The prime factor (without multiplicity) of the first composite 4 is 2; the second composite is 6 with prime factors 3 and 2, so 2+2+3=7, the prime sum of prime factors at N=6.

%t Module[{nn=700,cmps},cmps=Select[Range[nn],CompositeQ];Select[ Thread[ {cmps,Accumulate[Total[FactorInteger[#][[All,1]]]&/@cmps]}],PrimeQ[ #[[2]]]&]][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 22 2020 *)

%Y Cf. A140610.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, May 19 2008