A282940 - OEIS

%I #25 Apr 29 2024 09:38:09

%S 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,

%T 30,46,24,14,33,10,54,56,58,39,11,62,42,66,70,24,21,74,30,51,78,40,54,

%U 82,13,57,86,35,88,30,94,24,14,66,40,102,69,104,106,110,56

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

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

%H Amiram Eldar, <a href="/A282940/b282940.txt">Table of n, a(n) for n = 1..10000</a>

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

%F From _Amiram Eldar_, Apr 29 2024: (Start)

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

%F 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)

%t 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 *)

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

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Feb 25 2017

%E More terms from _Peter J. C. Moses_, Feb 25 2017