A187878 Numbers k such that sopfr(k + omega(k)) = sopfr(k), where sopfr(i) = A001414(i) and omega(i) = A001221(i).

5, 8, 10, 125, 231, 250, 470, 1846, 2844, 2856, 3570, 5126, 5320, 7473, 8687, 12555, 12573, 16740, 16764, 17877, 18630, 20601, 21620, 22011, 24823, 27468, 28861, 31941, 33120, 37053, 42315, 42588, 43761, 49404, 58078, 61072, 67728, 68320, 75042, 79947, 84660, 86427, 92432, 97723, 98802, 99580

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Antonio Roldán, hojaynumeros.blogspot.com.

Eric Weisstein's World of Mathematics, Prime Factor.

Eric Weisstein's World of Mathematics, Sum of Prime Factors.

Wikipedia, Additive function.

Example

omega(5126)=3, (5126=2*11*233), 5126+3=5129, sopfr(5126)=2+11+233=246,
5129=23*223, sopfr(5129)=2+223=246

Mathematica

omega[n_] := If[n < 2, 0, Length[FactorInteger[n]]]; sopfr[n_] := Module[{p, e}, If[n < 2, 1, {p, e} = Transpose[FactorInteger[n]]; Total[p*e]]]; Select[Range[2, 100000], sopfr[#] == sopfr[# + omega[#]] &] (* T. D. Noe, Mar 14 2011 *)

Prog

(PARI) sopfr(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) }
{ for (n=1, 10^6, if (sopfr(n)==sopfr(n+omega(n)), print1(n, ", "))); }
/* Antonio Roldán, Oct 23 2012 */

Crossrefs

Cf. A001221 (omega), A001414 (sopfr: integer logarithm), A187877.

Sequence in context: A057154 A072524 A240968 * A191233 A314386 A189577

Adjacent sequences: A187875 A187876 A187877 * A187879 A187880 A187881

Keyword

nonn,changed

Author

Antonio Roldán, Mar 14 2011

Extensions

Extended by T. D. Noe, Mar 14 2011

Status

approved