A076525 Numbers n such that sopf(n) = sopf(n+1) - sopf(n-1), where sopf(x) = sum of the distinct prime factors of x.
4, 22, 57, 900, 1551, 1920, 4194, 6279, 10857, 19648, 20384, 32016, 63656, 65703, 83271, 84119, 86241, 105570, 145237, 181844, 271328, 271741, 316710, 322953, 331976, 345185, 379659, 381430, 409915, 424503, 490255, 524476, 542565, 550271
Offset: 1
Keywords
Examples
The sum of the distinct prime factors of 22 is 2 + 11 = 13; the sum of the distinct prime factors of 23 is 23; the sum of the distinct prime factors of 21 is 3 + 7 = 10; and 13 = 23 - 10. Hence 22 belongs to the sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k:k in [3..560000]| &+PrimeDivisors(k) eq &+PrimeDivisors(k+1)-&+PrimeDivisors(k-1)]; // Marius A. Burtea, Oct 10 2019
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Mathematica
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == p[ # + 1] - p[ # - 1] &]
Extensions
Edited and extended by Ray Chandler, Feb 13 2005