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

2, 8, 120, 168, 175, 247, 860, 1044, 1444, 1659, 1849, 3626, 3834, 4233, 4300, 4345, 4814, 6867, 8240, 14905, 23287, 24476, 28919, 29087, 29464, 30457, 30650, 33725, 34945, 35585, 37214, 49468, 52206, 54900, 58113, 62049, 63440, 65631, 68264

Offset: 1

Author

Jason Earls, Sep 08 2001

Keywords

• nonn

Comments

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

Prime factors counted without multiplicity. - Harvey P. Dale, Dec 26 2015

Examples

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

Links

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

Crossrefs

Cf. A006145, A008472.

Programs

Mathematica

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 *)

PARI

sopf(n,s,fac,i)=fac=factor(n); for(i=1,matsize(fac)[1],s=s+fac[i,1]); return(s);
j=[]; for(n=1,100000, if(sopf(n)+1==sopf(n+1), j=concat(j,n))); j

PARI

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