A282940 Largest non-infinitary divisor of A162643(n) having no non-infinitary divisors.

2, 3, 6, 8, 6, 10, 5, 14, 8, 6, 22, 15, 24, 7, 10, 26, 30, 21, 8, 34, 24, 15, 38, 40, 27, 42, 30, 46, 24, 14, 33, 10, 54, 56, 58, 39, 11, 62, 42, 66, 70, 24, 21, 74, 30, 51, 78, 40, 54, 82, 13, 57, 86, 35, 88, 30, 94, 24, 14, 66, 40, 102, 69, 104, 106, 110, 56

Offset: 1

Author

Vladimir Shevelev, Feb 25 2017

Keywords

• nonn

Comments

Or largest term of A036537 dividing A162643(n) (cf. our comment in A036537).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A036537, A162643, A282900, A327839, A372379.

Programs

Mathematica

f[p_, e_] := p^(2^Floor[Log2[e + 1]] - 1); s[1] = Nothing; s[n_] := Module[{v = Times @@ f @@@ FactorInteger[n]}, If[v == n, Nothing, v]]; Array[s, 300] (* Amiram Eldar, Apr 29 2024 *)

Formula

a(n) = A036537(m), where m = max{k: A036537(k)|A162643(n)}.

From Amiram Eldar, Apr 29 2024: (Start)

a(n) = A372379(A162643(n)).

Sum_{k=1..n} a(k) ~ ((c-d)/(1-d)^2) * n^2 / 2, where d = A327839 and c = 0.7907361848... is the constant in the asymptotic formula in A372379. (End)

Extensions

More terms from Peter J. C. Moses, Feb 25 2017