A307876 - OEIS

%I #45 Nov 08 2024 07:20:13

%S 8,16,64,24,4096,60,144,384,16777216,1073741824,240,360,4398046511104,

%T 98304,9216,18014398509481984,13824,6291456,840,31104,2160,402653184,

%U 19342813113834066795298816,1237940039285380274899124224,5760,884736,61440,37748736,412316860416

%N a(n) is the smallest m such that there are prime(n) Pythagorean triangles with a leg (not hypotenuse) of length m, or -1 if no such m exists.

%C a(n) is the smallest m such that A046079(m) = n-th prime.

%C All a(n) > 10^6 for 8 < n < 30 were provided by _Amiram Eldar_.

%C When prime(n) is a Sophie Germain prime (A005384), then a(n) = 2^(prime(n)+1).

%C a(n) = m if m is the smallest solution of the equation A046079(m) = prime(n). This equation can be solved by inversing the formula for A046079(n) given by Temple Keller.

%H Amiram Eldar, <a href="/A307876/b307876.txt">Table of n, a(n) for n = 1..39</a>

%F Let prime(n)*2 + 1 be (2*a0 - 1)*(2*a1 + 1)*(2*a2 + 1)*(2*a3 + 1)*...*(2*ak + 1). Then a(n) = (2^a0)*(p1^a1)*...*(pk^ak).

%e 4096 is the smallest integer that can be the harmonic mean of two different integers in 11 different ways. A000040(5) = A046079(4096) = 11, so a(5) = 4096.

%Y Cf. A000040, A046079.

%K nonn

%O 1,1

%A _Bob Andriesse_, May 02 2019