login
a(n) = A062457(A000043(n)) = prime(A000043(n))^A000043(n), where A000043 gives the exponent of the n-th Mersenne prime.
28

%I #28 Oct 22 2024 05:43:04

%S 9,125,161051,410338673,925103102315013629321,

%T 1271991467017507741703714391419,49593099428404263766544428188098203,

%U 165163983801975082169196428118414326197216835208154294976154161023

%N a(n) = A062457(A000043(n)) = prime(A000043(n))^A000043(n), where A000043 gives the exponent of the n-th Mersenne prime.

%C If there are no odd perfect numbers, then the terms give all solutions n > 1 to A323244(n) = 0.

%C Conversely, if these are all numbers k > 1 that satisfy A323244(k) = 0 (which can be proved if one can show, for example, that no number in A007916 can satisfy the equation), then no odd perfect numbers exist. See also A336700. - _Antti Karttunen_, Jan 12 2024

%H Amiram Eldar, <a href="/A324201/b324201.txt">Table of n, a(n) for n = 1..12</a>

%F a(n) = A062457(A000043(n)).

%F A323244(a(n)) = 0.

%F a(n) = A005940(1+A000396(n)). [Provided no odd perfect numbers exist]

%t Prime[#]^#&/@MersennePrimeExponent[Range[8]] (* _Harvey P. Dale_, Mar 15 2024 *)

%Y Cf. A000043, A000396, A005940, A007916, A062457, A323244, A324200.

%Y Subsequence of A001597.

%Y Cf. also A336700, A368989.

%K nonn,changed

%O 1,1

%A _Antti Karttunen_, Feb 18 2019