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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..2400

Example

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.

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 *)

Crossrefs

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

Sequence in context: A230791 A087425 A031648 * A126301 A205176 A205275

Adjacent sequences: A075781 A075782 A075783 * A075785 A075786 A075787

Keyword

nonn

Author

_Joseph L. Pe_, Oct 18 2002

Extensions

Edited and extended by _Ray Chandler_, Feb 13 2005

Status

approved