OFFSET
1,1
COMMENTS
Sum of factors of a(n) if semiprime (product 2*p, with p prime).
This sequence is also subsequence of A045835, because sopfr(omega(a(n))) = omega(sopfr(a(n))): sopfr(omega(a(n)))=sopfr(2)=2, and omega(sopfr(a(n)))=omega(2*p)=2 (p prime, p>2, average prime factor).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
133 is in the sequence because 133 is a squarefree semiprime: 133=7*19, and (7+19)/2=13, a prime number.
MAPLE
N:= 10000: # for terms <= N
Primes:= select(isprime, [seq(i, i=3..N/3)]):
SP:= [seq(seq([p, q], q = select(`<=`, Primes, min(p-1, N/p))), p=Primes)]:
B:= select(t -> isprime((t[1]+t[2])/2), SP):
sort(map(t -> t[1]*t[2], B)); # Robert Israel, Dec 14 2019
MATHEMATICA
Select[Select[Range@ 1330, SquareFreeQ@ # && PrimeOmega@ # == 2 &], PrimeQ@ Mean[First /@ FactorInteger@ #] &] (* Michael De Vlieger, Mar 30 2016 *)
PROG
(PARI)
sopf(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }
{for (n=6, 2*10^3, if(bigomega(n)==2&&omega(n)==2, m=sopf(n)/2; if(m==truncate(m), if(isprime(m), print1(n, ", ")))))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, Mar 30 2016
STATUS
approved