A273057 Largest term in A067128 having greatest prime divisor prime(n).

8, 108, 4320, 151200, 3326400, 108108000, 10291881600, 586637251200, 53970627110400, 5869305698256000, 667144414368432000, 26928374543598528000, 3036174229790734032000, 522221967524006253504000, 159538811078583910445472000, 16911113974329894507220032000, 1164048345233041071913645536000, 304315495968066451657424475840000, 28544793521804633165466415833792000, 2026680340048128954748115524199232000

Offset: 1

Author

David A. Corneth and Vladimir Shevelev, May 14 2016

Keywords

• nonn

Comments

By the theorem of Vladimir Shevelev mentioned in sequence A273015, such an element exists for each prime.

Crossrefs

Cf. A273015, A273016, A273018.

Programs

Mathematica

a = {}; b = {0}; Do[If[# >= Max@ b, AppendTo[a, k] && AppendTo[b, #]] &@
DivisorSigma[0, k], {k, 10^7}]; TakeWhile[Table[SelectFirst[Reverse@ a,
FactorInteger[#][[-1, 1]] == Prime@ n &], {n, 6}], # < Max@ a &] (* Michael De Vlieger, May 14 2016 *)