A072751 Greatest of the most frequent prime factors of squarefree numbers <= n; a(1)=1.

1, 2, 3, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

• nonn
• nice

Comments

a(n)=2 for n>14.

Links

• Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.

Crossrefs

Cf. A005117, A072747, A072748, A072749, A072750.

Programs

Mathematica

max = 200; primeFactors = FactorInteger[#][[All, 1]]& /@ Select[Range[max], SquareFreeQ]; a[n_] := Sort[ Tally[ Take[ primeFactors, n] // Flatten], Which[#1[[2]] > #2[[2]], True, #1[[2]] == #2[[2]], #1[[1]] > #2[[1]], True, False]& ][[1, 1]]; Table[a[n], {n, 1, primeFactors // Length}] (* Jean-François Alcover, Oct 14 2013 *)