A105779 -id:A105779 - 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

A235425 Numbers k such that between k and the next prime there are gpf(k) numbers, where gpf(k) denotes the largest prime factor of k.

Original entry on oeis.org

8, 64, 128, 625, 729, 1701, 2625, 3025, 4096, 6435, 8505, 10115, 12675, 14641, 17303, 19343, 19683, 19845, 21125, 25515, 25725, 26325, 26741, 27783, 32768, 33075, 33275, 34075, 35721, 38025, 39375, 42525, 43875, 50193, 59319, 60835, 61731, 70805, 75411, 75803

Offset: 1

Giovanni Resta, Jan 10 2014

nonn

			64 = 2^6, whose largest prime factor is 2, is in the sequence because between 64 and 67 (the next prime) there are 2 numbers, 65 and 66.

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

Cf. A050765, A105779.

Select[Range[10^5], NextPrime[#] - # == 1 + FactorInteger[#][[-1, 1]] &]

gpf(n)=n=factor(n)[,1];n[#n]
is(n)=nextprime(n)-n==gpf(n)+1 \\ 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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