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Numbers k such that sopf(k) = 2*sopf(k+1), where sopf(k) = A008472.
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%I #23 Nov 17 2019 03:51:09

%S 99,155,689,1106,1517,1524,3014,3403,3479,5809,6478,6723,8606,9143,

%T 9454,9797,10126,11771,12283,12382,13112,13969,14150,17422,19303,

%U 22184,24856,27466,28119,28529,35927,36464,37512,41904,44505,45016,45506

%N Numbers k such that sopf(k) = 2*sopf(k+1), where sopf(k) = A008472.

%H Amiram Eldar, <a href="/A064112/b064112.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..600 from Harry J. Smith)

%e sopf(689)=66, 2*sopf(690)=66.

%o (PARI) sopf(n, s, fac, i) = fac=factor(n); for(i=1,matsize(fac)[1],s=s+fac[i,1]); return(s);

%o j=[]; for(n=1,50000, if(sopf(n)==2*sopf(n+1),j=concat(j,n))); j

%o (PARI) sopf(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }

%o { n=0; sm=sopf(1); for (m=1, 10^9, sp=sopf(m + 1); if (sm==2*sp, write("b064112.txt", n++, " ", m); if (n==600, break)); sm=sp ) } \\ _Harry J. Smith_, Sep 07 2009

%Y Cf. A008472 (sopf).

%K nonn

%O 1,1

%A _Jason Earls_, Sep 08 2001