A394084 - OEIS

A394084

a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive integer k whose greatest prime factor matches the greatest prime factor of the sum of the greatest prime factors of the previous terms.

1, 2, 3, 6, 9, 12, 5, 10, 15, 20, 7, 14, 21, 28, 35, 42, 11, 22, 33, 44, 55, 66, 13, 26, 39, 52, 65, 78, 17, 34, 51, 68, 85, 102, 19, 38, 57, 76, 95, 114, 23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 29, 58, 87, 116, 145, 174, 203, 232, 31, 62, 93, 124, 155, 186, 217, 248

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OFFSET

1,2

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

EXAMPLE

a(3) = 3 since gpf(1) + gpf(2) = 3 and gpf(3) = 3.

a(4) = 6 since gpf(1) + gpf(2) + gpf(3) = 6 and gpf(6) = 3.

MATHEMATICA

s={1, 2}; g={1, 2}; Do[k=2; Until[!MemberQ[s, k]&&FactorInteger[k][[ -1, 1]]==FactorInteger[Total[g]][[-1, 1]], k++]; AppendTo[s, k]; AppendTo[g, FactorInteger[k][[-1, 1]]], {n, 64}]; s (* James C. McMahon, Apr 14 2026 *)

PROG

(PARI) \\ See Links section.

CROSSREFS

Cf. A006530, A392975.

Sequence in context: A029805 A082007 A064417 * A191981 A131975 A288754

Adjacent sequences: A394080 A394081 A394083 * A394085 A394086 A394087

KEYWORD

nonn

AUTHOR

Jean-Marc Rebert, Apr 07 2026

STATUS

approved