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Numbers k such that z(k) = j(k), where z(k) = sopf(k - d(k)), j(k) = d(sopf(k) + k), sopf(k) = A008472(k) and d(k) = A000005(k).
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%I #15 Jun 24 2018 21:12:00

%S 6,24,40,516,532,679,1219,1581,1790,2196,2212,3060,3182,4120,4266,

%T 5816,9084,9812,11648,11911,13532,16488,16904,17016,17436,20448,20460,

%U 21129,23962,25356,26016,34307,34856,41624,42348,44392,48420,50696

%N Numbers k such that z(k) = j(k), where z(k) = sopf(k - d(k)), j(k) = d(sopf(k) + k), sopf(k) = A008472(k) and d(k) = A000005(k).

%H Harry J. Smith, <a href="/A063961/b063961.txt">Table of n, a(n) for n = 1..375</a>

%o (PARI) sumprime(n,s,fac,i) = fac=factor(n); for(i=1,matsize(fac)[1],s=s+fac[i,1]); return(s); z(n)=sumprime(n-numdiv(n)); d(n)=numdiv(sumprime(n)+n); for(n=1,10^6, if(d(n)==z(n),print(n)))

%o (PARI) sumprime(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) } z(n)= { sumprime(n - numdiv(n)) } d(n)= { numdiv(sumprime(n) + n) } { n=0; for (m=1, 10^9, if(d(m)==z(m), write("b063961.txt", n++, " ", m); if (n==375, break)) ) } \\ _Harry J. Smith_, Sep 04 2009

%K nonn

%O 1,1

%A _Jason Earls_, Sep 04 2001