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Sum of the prime factors of k equals half the sum of the prime factors of k + 1.
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%I #6 Jan 15 2022 23:32:09

%S 90,208,867,1161,1674,2139,2295,2821,3683,9675,10374,11357,14823,

%T 17685,20436,23750,23895,28035,39039,39962,43687,43813,47564,63624,

%U 75615,79281,97382,100855,103246,119350,124749,126575,136344,157250,178503,201877,218368,220375

%N Sum of the prime factors of k equals half the sum of the prime factors of k + 1.

%e The sum of the prime factors of 90 = 2 * 3^2 * 5 is 2 + 3 + 5 = 10; the sum of the prime factors of 91 = 7 * 13 = 20. Hence 90 belongs to the sequence.

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

%o (PARI) is(k) = 2*vecsum(factor(k)[,1]) == vecsum(factor(k+1)[,1]); \\ _Jinyuan Wang_, Jan 15 2022

%Y Cf. A008472.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 18 2002

%E Offset changed to 1 and more terms from _Jinyuan Wang_, Jan 15 2022