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A064111 Numbers k such that sopf(k) + 1 = sopf(k+1), where sopf(k) = A008472(k).

%I A064111 #26 Nov 17 2019 03:50:39
%S A064111 2,8,120,168,175,247,860,1044,1444,1659,1849,3626,3834,4233,4300,4345,
%T A064111 4814,6867,8240,14905,23287,24476,28919,29087,29464,30457,30650,33725,
%U A064111 34945,35585,37214,49468,52206,54900,58113,62049,63440,65631,68264
%N A064111 Numbers k such that sopf(k) + 1 = sopf(k+1), where sopf(k) = A008472(k).
%C A064111 Also k such that z(k) = z(k+1) where z(k) = k - sopf(k).
%C A064111 Prime factors counted without multiplicity. - _Harvey P. Dale_, Dec 26 2015
%H A064111 Amiram Eldar, <a href="/A064111/b064111.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%e A064111 sopf(8) + 1 = 3, sopf(8 + 1) = 3.
%t A064111 Flatten[Position[Partition[Table[Total[Transpose[FactorInteger[n]] [[1]]], {n, 2,70000}],2,1],_?(#[[1]]+1==#[[2]]&),{1},Heads->False]]+1 (* _Harvey P. Dale_, Dec 26 2015 *)
%o A064111 (PARI) sopf(n,s,fac,i)=fac=factor(n); for(i=1,matsize(fac)[1],s=s+fac[i,1]); return(s);
%o A064111 j=[]; for(n=1,100000, if(sopf(n)+1==sopf(n+1), j=concat(j,n))); j
%o A064111 (PARI) z(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(n - s) }
%o A064111 { n=0; zm=z(1); for (m=1, 10^9, zp=z(m + 1); if (zm==zp, write("b064111.txt", n++, " ", m); if (n==1000, break)); zm=zp ) } \\ _Harry J. Smith_, Sep 07 2009
%Y A064111 Cf. A006145, A008472.
%K A064111 nonn
%O A064111 1,1
%A A064111 _Jason Earls_, Sep 08 2001