A075784 - OEIS

%I #11 Feb 22 2020 13:20:35

%S 23156,59785,72521,98426,362231,480223,506123,1049790,1077252,1133953,

%T 1202068,1277411,1327229,1627040,2200058,2317712,2368026,3610497,

%U 4174012,5668196,6302128,6324778,6946075,7179599,7786163,8053816

%N 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.

%H Amiram Eldar, <a href="/A075784/b075784.txt">Table of n, a(n) for n = 1..2400</a>

%e 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.

%t p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[5, 10^5], p[ # - 1] + p[ # - 2] + p[ # - 3] == p[ # ] &]

%t Flatten[Position[Partition[Table[Total[FactorInteger[n][[All,1]]],{n,8054000}],4,1],_?(Total[Most[#]]==Last[#]&)]//Quiet]+3 (* _Harvey P. Dale_, Feb 22 2020 *)

%Y Cf. A008472, A075565, A075846, A076525, A076527, A076531, A076532, A076533.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 18 2002

%E Edited and extended by _Ray Chandler_, Feb 13 2005