A187877 Numbers k such that sopfr(k + bigomega(k)) = sopfr(k).

1, 5, 10, 45, 60, 128, 231, 308, 470, 847, 1846, 3570, 4284, 4740, 5126, 5688, 6171, 6650, 7473, 7980, 8687, 9310, 9964, 10640, 11172, 12896, 17877, 19716, 22011, 22736, 23280, 23836, 24823, 33480, 34335, 36384, 37260, 41202, 42315, 43761, 44480

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Antonio Roldán, hojaynumeros.blogspot.com

Wikipedia, Additive function

Example

308 is a term because bigomega(308)=4 (308=2*2*7*11), 308 + 4 = 312, sopfr(308) = 2 + 2 + 7 + 11 = 22, 312 = 2*2*2*3*13, sopfr(312) = 2 + 2 + 2 + 3 + 13 = 22.

Maple

A001414 := proc(n) if n = 1 then 0; else f := ifactors(n)[2] ; add( op(1, i)*op(2, i), i=f) ; end if; end proc:
isA187877 := proc(n) local m; m := n+numtheory[bigomega](n) ; is(A001414(n)=A001414(m)) ; end proc:
for n from 1 to 50000 do if isA187877(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Mar 14 2011

Mathematica

soprQ[n_]:=Total[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[n]]] == Total[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[n+PrimeOmega[n]]]]; Select[Range[50000], soprQ] (* Harvey P. Dale, Jan 21 2013 *)

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+bigomega(n)), print1(n, ", "))); }
/* Antonio Roldán, Oct 23 2012 */

Crossrefs

Cf. A001222 (bigomega), A001414 (sopfr).

Cf. A187878.

Sequence in context: A186031 A305246 A316546 * A328605 A122173 A083515

Adjacent sequences: A187874 A187875 A187876 * A187878 A187879 A187880

Keyword

nonn

Author

Antonio Roldán, Mar 14 2011

Status

approved