A235425 -id:A235425 - cp's OEIS frontend

A050765 Composite n added to sum of its prime factors is nextprime(n).

38400, 59290, 89700, 93639, 155952, 356400, 682080, 1226907, 1468320, 1648640, 2592000, 2995200, 3595500, 3933644, 5845203, 5967360, 8860995, 8953560, 9748480, 11351340, 12819224, 13226976, 13712490, 16193520, 18375000, 19294436, 21206016, 25259520, 28297500

Offset: 1

Patrick De Geest, Sep 15 1999

			nextprime(93639) = 93639 + (3+7+7+7+7+13) = 93683.

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..1033 (terms < 10^12, first 500 terms from Donovan Johnson)
C. Rivera, See also related puzzle

Cf. A050766, A050703, A050710, A105779, A235425.

Reap[For[n = 4, n <= 2*10^7, n = If[PrimeQ[n+1], n+2, n+1], If[n + Total[Times @@@ FactorInteger[n] ] == NextPrime[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 18 2013 *)
cspfQ[n_]:=CompositeQ[n]&&NextPrime[n]==n+Total[Flatten[Table[ #[[1]], #[[2]]] &/@FactorInteger[n]]]; Select[Range[29*10^6],cspfQ] (* Harvey P. Dale, Oct 14 2017 *)

Offset corrected by Donovan Johnson, Oct 18 2013

A105779 Numbers n such that n + (sum of prime factors of n) = next prime after n.

Original entry on oeis.org

24, 48, 54, 144, 288, 384, 648, 972, 1260, 1728, 1792, 1936, 1944, 2304, 3584, 5184, 6250, 6912, 7168, 8748, 8788, 9216, 9604, 10000, 10125, 10816, 11760, 13122, 13824, 17640, 21632, 21952, 23328, 24255, 25088, 26244, 27648, 33264, 35937, 37752

Offset: 1

Joseph L. Pe, May 06 2005

nonn

			24 + (sum of prime factors of 24) = 24 + (2 + 3) = 29, the next prime after 24. So 24 belongs to the sequence.

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

Cf. A050765, A235425.

Select[Range[2, 10^5], NextPrime[#] == # + Plus @@ First /@ FactorInteger@# &]

sopf(n)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
is(n)=nextprime(n+1)-n==sopf(n) \\ Charles R Greathouse IV, Jan 10 2014

cp's OEIS Frontend

A050765 Composite n added to sum of its prime factors is nextprime(n).

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