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

1, 4, 12, 28, 30, 52, 55, 65, 68, 76, 95, 145, 155, 185, 205, 822, 894, 2779, 2863, 8392, 23481, 24093, 24237, 64270, 174691, 174779, 1301989, 1302457, 3523478, 9554955, 9555045, 9556455, 70111213, 70111247, 189960426, 514269523, 514269599, 10246934786

Offset: 1

Author

Jason Earls, Oct 02 2001

Keywords

• nonn

Comments

No further terms < 800000. - Klaus Brockhaus, Oct 05 2001

Links

• Giovanni Resta, Table of n, a(n) for n = 1..42 (terms < 2*10^12).

Crossrefs

Cf. A008472, A000720.

Programs

Mathematica

sopf[n_] := If[n==1, 0, Total[First /@ FactorInteger[n]]]; Select[Range[10^4], PrimePi@ # == sopf@ # &] (* Giovanni Resta, Mar 28 2017 *)

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

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

Extensions

More terms from Klaus Brockhaus, Oct 05 2001

a(27)-a(29) from Harry J. Smith, Sep 14 2009

a(30)-a(38) from Giovanni Resta, Mar 28 2017