A307876 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.

8, 16, 64, 24, 4096, 60, 144, 384, 16777216, 1073741824, 240, 360, 4398046511104, 98304, 9216, 18014398509481984, 13824, 6291456, 840, 31104, 2160, 402653184, 19342813113834066795298816, 1237940039285380274899124224, 5760, 884736, 61440, 37748736, 412316860416

Offset

1,1

Comments

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

All a(n) > 10^6 for 8 < n < 30 were provided by Amiram Eldar.

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

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..39

Formula

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).

Example

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.

Crossrefs

Cf. A000040, A046079.

Sequence in context: A212764 A133581 A222544 * A166638 A356961 A339355

Adjacent sequences: A307873 A307874 A307875 * A307877 A307878 A307879

Keyword

nonn

Author

Bob Andriesse, May 02 2019

Status

approved