A063996 Numbers k such that ud(k) = sopf(k)-1, where ud(k)=A034444(k) and sopf(k)=A008472(k).

3, 6, 9, 12, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, 144, 162, 192, 210, 216, 243, 288, 324, 384, 420, 432, 486, 576, 630, 648, 729, 768, 840, 864, 972, 1050, 1152, 1260, 1296, 1458, 1470, 1536, 1680, 1728, 1890, 1944, 2100, 2187, 2304, 2520, 2592, 2916

Offset: 1

Author

Jason Earls, Sep 06 2001

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (term 1..1000 from Harry J. Smith)

Crossrefs

Cf. A034444, A008472.

Programs

PARI

sopf(n,s,fac,i)=fac=factor(n); for(i=1,matsize(fac)[1], s=s+fac[i,1]); return(s); ud(n) = 2^omega(n); j=[]; for(n=1,7000, if(ud(n)==sopf(n)-1, 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 (2^omega(m)==sopf(m) - 1, write("b063996.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 05 2009