A075784 Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2) + sopf(n-3), where sopf(x) = sum of the distinct prime factors of x.
23156, 59785, 72521, 98426, 362231, 480223, 506123, 1049790, 1077252, 1133953, 1202068, 1277411, 1327229, 1627040, 2200058, 2317712, 2368026, 3610497, 4174012, 5668196, 6302128, 6324778, 6946075, 7179599, 7786163, 8053816
Offset: 1
Keywords
Examples
The sum of the distinct prime factors of 23156 is 2 + 7 + 827 = 836; the sum of the distinct prime factors of 23155 is 5 + 11 + 421 = 437; the sum of the distinct prime factors of 23154 is 2 + 3 + 17 + 227 = 249; the sum of the distinct prime factors of 23153 is 13 + 137 = 150; and 836 = 437 + 249 + 150. Hence 23156 belongs to the sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..2400
Programs
-
Mathematica
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[5, 10^5], p[ # - 1] + p[ # - 2] + p[ # - 3] == p[ # ] &] Flatten[Position[Partition[Table[Total[FactorInteger[n][[All,1]]],{n,8054000}],4,1],?(Total[Most[#]]==Last[#]&)]//Quiet]+3 (* _Harvey P. Dale, Feb 22 2020 *)
Extensions
Edited and extended by Ray Chandler, Feb 13 2005