A187877 - OEIS

%I #33 Jan 29 2019 09:21:08

%S 1,5,10,45,60,128,231,308,470,847,1846,3570,4284,4740,5126,5688,6171,

%T 6650,7473,7980,8687,9310,9964,10640,11172,12896,17877,19716,22011,

%U 22736,23280,23836,24823,33480,34335,36384,37260,41202,42315,43761,44480

%N Numbers k such that sopfr(k + bigomega(k)) = sopfr(k).

%H Harvey P. Dale, <a href="/A187877/b187877.txt">Table of n, a(n) for n = 1..500</a>

%H Antonio Roldán, <a href="http://hojaynumeros.blogspot.com/2011/03/parientes-de-ruth-y-aaron.html">hojaynumeros.blogspot.com</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Additive_function">Additive function</a>

%e 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.

%p 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:

%p isA187877 := proc(n) local m; m := n+numtheory[bigomega](n) ; is(A001414(n)=A001414(m)) ; end proc:

%p for n from 1 to 50000 do if isA187877(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Mar 14 2011

%t 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 *)

%o (PARI)

%o sopfr(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) }

%o { for (n=1, 10^6, if (sopfr(n)==sopfr(n+bigomega(n)), print1(n,", "))); }

%o /* _Antonio Roldán_, Oct 23 2012 */

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

%Y Cf. A187878.

%K nonn

%O 1,2

%A _Antonio Roldán_, Mar 14 2011