A064010 Numbers k such that sopf(k) = d(k) where d(k) = A001223(k) and sopf(k) = A008472(k).

2, 64, 135, 154, 168, 256, 350, 512, 539, 1029, 1350, 1875, 2106, 2268, 2646, 2673, 2736, 2976, 4375, 6000, 6076, 6517, 6880, 7680, 9680, 10092, 10584, 14000, 14406, 14580, 14976, 17500, 18522, 20412, 26000, 26068, 26112, 26620, 27216, 28812

Offset: 1

Author

Jason Earls, Sep 07 2001

Keywords

• easy
• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2000 (first 150 terms from Harry J. Smith)

Crossrefs

Cf. A001223, A008472.

Programs

PARI

sopf(n,s,fac,i)=fac=factor(n); for(i=1,matsize(fac)[1], s=s+fac[i,1]); return(s);
d(n) = prime(n+1)-prime(n);
j=[]; for(n=1,50000, if(sopf(n)==d(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) }
d(n)= { prime(n + 1) - prime(n) }
{ default(primelimit, 13500000); n=0; for (m=1, 10^9, if (sopf(m)==d(m), write("b064010.txt", n++, " ", m); if (n==150, break)) ) } \\ Harry J. Smith, Sep 05 2009