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PROG
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(PARI) smallf(q, nmax) = {my(qq=q, j=0); forprime (p=2, nmax, my(k=0); while (qq%p==0, k++; qq/=p); if (k>0, j++; )); [j, qq]};
a362957(upto) = {my(nfmax=0); for (n=1, upto, forprime (p=2, oo, my(f=p^n+1, s=smallf(f, p)); if (s[1]<n\3, next); my(nf=omega(s[2])+s[1]); if (nf>nfmax, print1(p, ", "); nfmax=nf; break)))};
a362957(12)
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