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A324201

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

9, 125, 161051, 410338673, 925103102315013629321, 1271991467017507741703714391419, 49593099428404263766544428188098203, 165163983801975082169196428118414326197216835208154294976154161023

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OFFSET

1,1

COMMENTS

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

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..12

FORMULA

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

A323244(a(n)) = 0.

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

MATHEMATICA

Prime[#]^#&/@MersennePrimeExponent[Range[8]] (* Harvey P. Dale, Mar 15 2024 *)

CROSSREFS

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

Subsequence of A001597.

Cf. also A336700, A368989.