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A072087
Least k such that A072084(k) = n.
3
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
1,2
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.
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
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 *)
PROG
(Haskell)
a072087 1 = 1
a072087 n = product $ map a061712 $ a027746_row n
-- Reinhard Zumkeller, Feb 10 2013
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Reinhard Zumkeller, Jun 14 2002
EXTENSIONS
More terms from David W. Wilson, Aug 03 2005
STATUS
approved