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A187878 Numbers n such that sopfr(n + omega(n)) = sopfr(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..46.

Antonio Roldán, hojaynumeros.blogspot.com

Wikipedia, Additive function

Eric W. Weisstein, Sum of Prime Factors

Eric W. Weisstein, Prime Factor

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. A187877.

Sequence in context: A057154 A072524 A240968 * A191233 A189577 A047700

Adjacent sequences:  A187875 A187876 A187877 * A187879 A187880 A187881

KEYWORD

nonn

AUTHOR

Antonio Roldán, Mar 14 2011

EXTENSIONS

Extended by T. D. Noe, Mar 14 2011

STATUS

approved

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Last modified December 4 16:52 EST 2016. Contains 278750 sequences.