A074213 Sum of the prime factors of k equals half the sum of the prime factors of k + 1.

90, 208, 867, 1161, 1674, 2139, 2295, 2821, 3683, 9675, 10374, 11357, 14823, 17685, 20436, 23750, 23895, 28035, 39039, 39962, 43687, 43813, 47564, 63624, 75615, 79281, 97382, 100855, 103246, 119350, 124749, 126575, 136344, 157250, 178503, 201877, 218368, 220375

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Example

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.

Mathematica

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

Prog

(PARI) is(k) = 2*vecsum(factor(k)[, 1]) == vecsum(factor(k+1)[, 1]); \\ Jinyuan Wang, Jan 15 2022

Crossrefs

Cf. A008472.

Sequence in context: A044422 A044803 A235081 * A231961 A237131 A363729

Adjacent sequences: A074210 A074211 A074212 * A074214 A074215 A074216

Keyword

nonn

Author

Joseph L. Pe, Oct 18 2002

Extensions

Offset changed to 1 and more terms from Jinyuan Wang, Jan 15 2022

Status

approved