A074964 Numbers k such that Max ( sigma(x*y) : 1 <= x <= k, 1 <= y <= k ) = sigma(k^2).

1, 2, 3, 4, 6, 8, 12, 18, 24, 60

Offset: 1

Author

Benoit Cloitre, Oct 05 2002

Keywords

• nonn
• more

Comments

Sequence is probably finite.

The next term in the sequence, if it exists, is larger than 40000. - Stewart Gordon, Sep 27 2011

Conjecture: subsequence of A066522, implying finiteness. - Reinhard Zumkeller, Nov 14 2011

Crossrefs

Cf. A000203, A066522, A065764, A074963.

Programs

Haskell

a074964 n = a074964_list !! (n-1)
a074964_list = filter (\x -> a074963 x == a065764 x) [1..]
-- Reinhard Zumkeller, Nov 14 2011

Maple

with(numtheory): s := proc(n) option remember: return sigma(n): end: a:= proc(n) option remember: if(n=0)then return 0: fi: return max(a(n-1),seq(s(x*n),x=1..n)): end: for n from 1 to 100 do if(a(n)=s(n^2))then printf("%d, ", n): end: od: # Nathaniel Johnston, Sep 26 2011

PARI

isok(k) = vecmax(setbinop((x,y)->sigma(x*y), [1..k])) == sigma(k^2); \\ Michel Marcus, Feb 03 2022

Formula

A074963(a(n)) = A065764(a(n)). - Reinhard Zumkeller, Nov 14 2011