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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == p[ # + 1] - p[ # - 1] &]

Prog

(Magma) [k:k in [3..560000]| &+PrimeDivisors(k) eq &+PrimeDivisors(k+1)-&+PrimeDivisors(k-1)]; // Marius A. Burtea, Oct 10 2019

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076527, A076531, A076532, A076533.

Sequence in context: A050773 A122241 A341375 * A089761 A098837 A104171

Adjacent sequences: A076522 A076523 A076524 * A076526 A076527 A076528

Keyword

nonn

Author

Joseph L. Pe, Oct 18 2002

Extensions

Edited and extended by Ray Chandler, Feb 13 2005

Status

approved