A072087 Least k such that A072084(k) = n.

1, 3, 7, 9, 31, 21, 127, 27, 49, 93, 3583, 63, 8191, 381, 217, 81, 131071, 147, 524287, 279, 889, 10749, 14680063, 189, 961, 24573, 343, 1143, 1073479679, 651, 2147483647, 243, 25081, 393213, 3937, 441, 266287972351, 1572861, 57337, 837

Offset: 1

Author

Reinhard Zumkeller, Jun 14 2002

Keywords

• nonn
• mult

Comments

If p is a Mersenne prime then a(p) = 2^p - 1 (A000120(2^n-1)=n), for other primes p: a(p) > 2^p - 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3322
• Index to divisibility sequences.

Crossrefs

Cf. A000120, A000043, A000668, A027746, A061712, A072084.

Programs

Haskell

a072087 1 = 1
a072087 n = product $ map a061712 $ a027746_row n
-- Reinhard Zumkeller, Feb 10 2013

Mathematica

s[n_] := s[n] = Module[{p = 2}, While[DigitCount[p, 2, 1] != n, p = NextPrime[p]]; p]; f[p_, e_] := s[p]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 22] (* Amiram Eldar, Nov 02 2023 *)

Formula

Completely multiplicative with a(p) = A061712(p). - David W. Wilson, Aug 03 2005

Sum_{n>=1} 1/a(n) = Product_{p prime} 1/(1 - 1/A061712(p)) = 1.82343415954263449963... . - Amiram Eldar, Nov 02 2023

Extensions

More terms from David W. Wilson, Aug 03 2005