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A187878 Numbers n such that sopfr(n + omega(n)) = sopfr(n). 1

%I

%S 5,8,10,125,231,250,470,1846,2844,2856,3570,5126,5320,7473,8687,12555,

%T 12573,16740,16764,17877,18630,20601,21620,22011,24823,27468,28861,

%U 31941,33120,37053,42315,42588,43761,49404,58078,61072,67728,68320,75042,79947,84660,86427,92432,97723,98802,99580

%N Numbers n such that sopfr(n + omega(n)) = sopfr(n).

%C Sopfr(n) = sum of the prime factors of n with multiplicity (integer logarithm)

%C omega(n) = number of prime divisors of n counted without multiplicity

%H Antonio Roldán, <a href="http://hojaynumeros.blogspot.com">hojaynumeros.blogspot.com</a>

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

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/SumofPrimeFactors.html"> Sum of Prime Factors</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>

%e omega(5126)=3, (5126=2*11*233), 5126+3=5129, sopfr(5126)=2+11+233=246,

%e 5129=23*223, sopfr(5129)=2+223=246

%t 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 *)

%o (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) }

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

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

%Y Cf. A187877.

%K nonn

%O 1,1

%A _Antonio Roldán_, Mar 14 2011

%E Extended by _T. D. Noe_, Mar 14 2011

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Last modified April 17 14:30 EDT 2014. Contains 240646 sequences.