A064111 - OEIS

%I #26 Nov 17 2019 03:50:39

%S 2,8,120,168,175,247,860,1044,1444,1659,1849,3626,3834,4233,4300,4345,

%T 4814,6867,8240,14905,23287,24476,28919,29087,29464,30457,30650,33725,

%U 34945,35585,37214,49468,52206,54900,58113,62049,63440,65631,68264

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

%C Also k such that z(k) = z(k+1) where z(k) = k - sopf(k).

%C Prime factors counted without multiplicity. - _Harvey P. Dale_, Dec 26 2015

%H 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 sopf(8) + 1 = 3, sopf(8 + 1) = 3.

%t 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 (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=1,100000, if(sopf(n)+1==sopf(n+1), j=concat(j,n))); j

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

%o { 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 Cf. A006145, A008472.

%K nonn

%O 1,1

%A _Jason Earls_, Sep 08 2001