A076527 Numbers n such that sopf(n) = sopf(n-1) - sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.

8, 66, 2883, 3264, 3552, 13872, 21386, 26896, 29698, 29768, 31980, 36567, 40517, 65305, 72012, 82719, 101639, 110848, 160230, 211646, 237136, 237568, 238303, 242606, 299186, 309960, 378014, 393208, 439105, 445795, 455182, 527078, 570021

Offset

1,1

Links

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

Example

The sum of the distinct prime factors of 66 is 2 + 3 + 11 = 16; the sum of the distinct prime factors of 65 is 5 + 13 = 18; the sum of the distinct prime factors of 64 is 2; and 16 = 18 - 2. Hence 66 belongs to the sequence.

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # ] == p[ # - 1] - p[ # - 2] &]

Prog

(Magma) [k:k in [4..571000]| &+PrimeDivisors(k-1) - &+PrimeDivisors(k-2) eq (&+PrimeDivisors(k))]; // Marius A. Burtea, Feb 12 2020

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076525, A076531, A076532, A076533.

Sequence in context: A121766 A052620 A052669 * A247112 A166815 A166797

Adjacent sequences: A076524 A076525 A076526 * A076528 A076529 A076530

Keyword

nonn

Author

Joseph L. Pe, Oct 18 2002

Extensions

Edited and extended by Ray Chandler, Feb 13 2005

Status

approved