cp's OEIS Frontend

A064444 Numbers k such that pi(k) = sopf(k) where sopf(k) is sum of distinct prime factors of k (A008472).

%I A064444 #22 Apr 13 2024 14:58:30
%S A064444 1,4,12,28,30,52,55,65,68,76,95,145,155,185,205,822,894,2779,2863,
%T A064444 8392,23481,24093,24237,64270,174691,174779,1301989,1302457,3523478,
%U A064444 9554955,9555045,9556455,70111213,70111247,189960426,514269523,514269599,10246934786
%N A064444 Numbers k such that pi(k) = sopf(k) where sopf(k) is sum of distinct prime factors of k (A008472).
%C A064444 No further terms < 800000. - _Klaus Brockhaus_, Oct 05 2001
%H A064444 Giovanni Resta, <a href="/A064444/b064444.txt">Table of n, a(n) for n = 1..42</a> (terms < 2*10^12).
%t A064444 sopf[n_] := If[n==1, 0, Total[First /@ FactorInteger[n]]]; Select[Range[10^4], PrimePi@ # == sopf@ # &] (* _Giovanni Resta_, Mar 28 2017 *)
%o A064444 (PARI) pi(x, c=0) = forprime(p=2,x,c++); c sopf(n, fac) = fac=factor(n); sum(i=1,matsize(fac)[1],fac[i,1]) j=[]; for(n=1,25000, if(pi(n)==sopf(n),j=concat(j,n))); j
%o A064444 (PARI) sopf(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) } { n=0; for (m=1, 10^9, if (primepi(m)==sopf(m), write("b064444.txt", n++, " ", m); if (n==100, break)) ) } \\ _Harry J. Smith_, Sep 14 2009
%Y A064444 Cf. A008472, A000720.
%K A064444 nonn
%O A064444 1,2
%A A064444 _Jason Earls_, Oct 02 2001
%E A064444 More terms from _Klaus Brockhaus_, Oct 05 2001
%E A064444 a(27)-a(29) from _Harry J. Smith_, Sep 14 2009
%E A064444 a(30)-a(38) from _Giovanni Resta_, Mar 28 2017