A083390 Integers m such that 2m + 1 divides lcm(1,3,5,...,2m - 1).

7, 10, 16, 17, 19, 22, 25, 27, 28, 31, 32, 34, 37, 38, 42, 43, 45, 46, 47, 49, 52, 55, 57, 58, 59, 61, 64, 66, 67, 70, 71, 72, 73, 76, 77, 79, 80, 82, 85, 87, 88, 91, 92, 93, 94, 97, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 112, 115, 117, 118, 122, 123, 124, 126

Offset

1,1

Comments

Also m for which A025547(m)=A025547(m+1). Query: a(n) seems to be equal to A030343(n+4) - 1. Is this true?

While any odd number>1 can be the leg of a primitive Pythagorean triangle, the m-th odd number 2m+1=A061346 forms leg common to more than one PPT. - Lekraj Beedassy, Jul 12 2006

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2500

Formula

a(n) = (A061346(n)-1)/2. - David Wasserman, Oct 26 2004

Example

10 is in the sequence because we have 2*10 - 1 = 19 and lcm(1,3,5,...,19)=166966608033225=7950790858725*21 which is divisible by 2*10 + 1 = 21.

Mathematica

Select[Range[150], Divisible[LCM@@Range[1, 2#-1, 2], 2#+1]&] (* Harvey P. Dale, Jan 22 2023 *)

Prog

(PARI) isok(n) = {lc = 1; for (i = 1, 2*n-1, lc = lcm(lc, i); ); return (lc % (2*n+1) == 0); } \\ Michel Marcus, Jul 27 2013
(Python)
from sympy import primepi, integer_nthroot
def A083390(n):
    def f(x): return int(n+sum(primepi(integer_nthroot((x<<1)|1, k)[0])-1 for k in range(1, x.bit_length()+1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 01 2025

Crossrefs

Cf. A080765.

Sequence in context: A120136 A020743 A088350 * A234093 A287567 A301451

Adjacent sequences: A083387 A083388 A083389 * A083391 A083392 A083393

Keyword

nonn

Author

Lekraj Beedassy, Jun 11 2003

Extensions

More terms from David Wasserman, Oct 26 2004

Status

approved