A075654 - OEIS

A075654

Numbers n such that n + sum of prime factors of n = (n+1) + sum of prime factors of (n+1).

%I #12 Sep 30 2019 09:10:58

%S 3,14,152,224,285,455,902,1518,2013,2079,4823,6655,7104,7584,8493,

%T 8532,9416,14344,15687,18569,20115,20163,20490,22351,25543,26123,

%U 28250,28564,30744,37305,37406,41261,45844,50609,51992,54137,56563,60651

%N Numbers n such that n + sum of prime factors of n = (n+1) + sum of prime factors of (n+1).

%H Amiram Eldar, <a href="/A075654/b075654.txt">Table of n, a(n) for n = 1..10000</a>

%e 14 + sum of prime factors of 14 = 14 + 2 + 7 = 23; 15 + sum of prime factors of 15 = 15 + 3 + 5 = 23; hence 14 belongs to the sequence.

%t s[n_] := n + Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^5], s[ # ] == s[ # + 1] &]

%t SequencePosition[Table[n+Total[FactorInteger[n][[All,1]]],{n,70000}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 23 2017 *)

%Y Cf. A008472, A075653.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 11 2002