A072087 - OEIS

%I #27 Nov 03 2023 08:40:57

%S 1,3,7,9,31,21,127,27,49,93,3583,63,8191,381,217,81,131071,147,524287,

%T 279,889,10749,14680063,189,961,24573,343,1143,1073479679,651,

%U 2147483647,243,25081,393213,3937,441,266287972351,1572861,57337,837

%N Least k such that A072084(k) = n.

%C 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.

%H Amiram Eldar, <a href="/A072087/b072087.txt">Table of n, a(n) for n = 1..3322</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.

%F Completely multiplicative with a(p) = A061712(p). - _David W. Wilson_, Aug 03 2005

%F Sum_{n>=1} 1/a(n) = Product_{p prime} 1/(1 - 1/A061712(p)) = 1.82343415954263449963... . - _Amiram Eldar_, Nov 02 2023

%t 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 *)

%o (Haskell)

%o a072087 1 = 1

%o a072087 n = product $ map a061712 $ a027746_row n

%o -- _Reinhard Zumkeller_, Feb 10 2013

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

%K nonn,mult

%O 1,2

%A _Reinhard Zumkeller_, Jun 14 2002

%E More terms from _David W. Wilson_, Aug 03 2005