A367952 Lexicographically earliest sequence of distinct positive integers such that n divides the sum of the distinct prime factors (sopf) of a(n - 1) + a(n), with a(1) = 1.

1, 3, 6, 9, 12, 23, 10, 5, 51, 39, 18, 17, 27, 43, 61, 26, 67, 11, 8, 83, 69, 16, 7, 88, 4, 65, 93, 22, 243, 128, 49, 38, 24, 121, 80, 75, 138, 79, 217, 102, 135, 50, 32, 91, 81, 48, 230, 28, 66, 225, 77, 158, 151, 178, 34, 125, 420, 97, 468, 62, 56, 475, 13, 170, 211, 94, 299, 311, 604, 45

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Éric Angelini, Sums of distinct prime factors, Personal blog, December 2023.

Example

a(1) + a(2) =  4, sopf(4)  =  2 and n=2 divides  2.
a(6) + a(7) = 33, sopf(33) = 14 and n=7 divides 14.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]|| Mod[Total[First/@FactorInteger[k+a[n-1]]], n]!=0, k++]; k); Array[a, 70]

Crossrefs

Cf. A008472.

Sequence in context: A153838 A143829 A194420 * A277823 A233155 A118519

Adjacent sequences: A367949 A367950 A367951 * A367953 A367954 A367955

Keyword

nonn

Author

Giorgos Kalogeropoulos and Eric Angelini, Dec 05 2023

Status

approved