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%I #11 Nov 21 2021 21:16:08
%S 4,42,60,72,618,1488,2730,4230,6762,8010,8232,8538,9282,12540,12822,
%T 13008,15582,19212,20898,24420,24918,26712,32718,41412,41610,43542,
%U 45318,46830,49530,50130,51060,53172,53550,55662,56598,58230,58368,61560,62130,69930,71712,72090,72222,75402,77688,78192
%N Members of A014574 with sum of prime factors (with multiplicity) also in A014574.
%C Numbers k such that k-1, k+1, A001414(k)-1 and A001414(k)+1 are all prime.
%H Robert Israel, <a href="/A349455/b349455.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 60 is a term because 60-1 = 59 and 60+1 = 61 are primes, A001414(60) = 2+2+3+5 = 12, and 12-1 = 11 and 12+1 = 13 are primes.
%p spf:= proc(n) local F,t;
%p F:= ifactors(n)[2];
%p add(t[1]*t[2],t=F)
%p end proc:
%p R:= 4: count:= 1:
%p for t from 6 by 6 while count < 100 do
%p if isprime(t-1) and isprime(t+1) then
%p s:= spf(t);
%p if isprime(s-1) and isprime(s+1) then
%p count:= count+1;
%p R:= R, t;
%p fi
%p fi
%p od:
%p R;
%t Select[Prime@Range@8000,PrimeQ[#+2]&&And@@PrimeQ[Total[Flatten[Table@@@FactorInteger[#+1]]]+{1,-1}]&]+1 (* _Giorgos Kalogeropoulos_, Nov 18 2021 *)
%Y Cf. A001414, A014574.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Nov 17 2021
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