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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A006145, A008472.

Sequence in context: A374380 A099292 A284967 * A112094 A009658 A147794

Adjacent sequences: A064108 A064109 A064110 * A064112 A064113 A064114

Keyword

nonn

Author

Jason Earls, Sep 08 2001

Status

approved