A368989 -id:A368989 - cp's OEIS frontend

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

Offset: 1

Antti Karttunen, Feb 18 2019

nonn

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

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

Cf. A000043, A000396, A005940, A007916, A062457, A323244, A324200.
Subsequence of A001597.
Cf. also A336700, A368989.

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

a(n) = A062457(A000043(n)).
A323244(a(n)) = 0.
a(n) = A005940(1+A000396(n)). [Provided no odd perfect numbers exist]

A368698 a(n) is the smallest positive k such that A005940(1+n) divides the oblong number k*(k+1).

Original entry on oeis.org

1, 1, 2, 3, 4, 2, 8, 7, 6, 4, 5, 3, 24, 8, 26, 15, 10, 6, 6, 4, 14, 5, 9, 8, 48, 24, 24, 8, 124, 26, 80, 31, 12, 10, 11, 7, 10, 6, 27, 15, 21, 14, 14, 15, 49, 9, 54, 15, 120, 48, 48, 24, 49, 24, 99, 8, 342, 124, 125, 27, 624, 80, 242, 63, 16, 12, 12, 11, 25, 11, 44, 7, 13, 10, 44, 20, 99, 27, 27, 15, 65, 21, 21, 20

Offset: 0

Antti Karttunen, Jan 11 2024

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A002378, A005940, A344005, A368699, A368700, A368693 (rgs-transform), A368988 (positions of records), A368989 (values of records).

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A344005(n) = { my(m=1); while((m*(m+1)) % n, m++); m; };
A368698(n) = A344005(A005940(1+n));

a(n) = A344005(A005940(1+n)).

For n >= 1, a(2^n) = A006093(n), a(A000225(n)) = A000225(n).

A368988 Positions of records in A368698.

Original entry on oeis.org

0, 2, 3, 4, 6, 12, 14, 24, 28, 56, 60, 112, 120, 124, 240, 248, 480, 488, 496, 992, 1000, 1008, 2016, 2032, 4016, 4024, 4064, 4080, 8112, 8128, 8160, 8176, 16312, 16320, 16352, 16368

Offset: 1

Antti Karttunen, Jan 12 2024

nonn

The even perfect numbers seem to occur here, as via Doudna-mapping they encode terms of A324201, which in turn have large values in A344005.

Cf. A000396, A324201, A344005, A368698, A368989 (values of records).

cp's OEIS Frontend

A324201 a(n) = A062457(A000043(n)) = prime(A000043(n))^A000043(n), where A000043 gives the exponent of the n-th Mersenne prime.

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A368698 a(n) is the smallest positive k such that A005940(1+n) divides the oblong number k*(k+1).

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A368988 Positions of records in A368698.

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