A093358 -id:A093358 - cp's OEIS frontend

A062457 a(n) = prime(n)^n.

2, 9, 125, 2401, 161051, 4826809, 410338673, 16983563041, 1801152661463, 420707233300201, 25408476896404831, 6582952005840035281, 925103102315013629321, 73885357344138503765449, 12063348350820368238715343, 3876269050118516845397872321

Offset: 1

Labos Elemer, Jul 09 2001

Heinz numbers of square integer partitions, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). - Gus Wiseman, Apr 14 2018
Main diagonal of A182944. - Omar E. Pol, Sep 12 2018
Second diagonal of A319075. - Omar E. Pol, Sep 13 2018

T. D. Noe, Table of n, a(n) for n = 1..100

Cf. A000040, A000312, A000720, A000961, A001222, A051674, A062006, A076146, A093358, A201614, A275024, A302242, A302493, A302498, A319075.

[NthPrime(n)^n : n in [1..20]]; // Wesley Ivan Hurt, Jan 18 2016

A062457:=n->ithprime(n)^n: seq(A062457(n), n=1..20); # Wesley Ivan Hurt, Jan 18 2016

Table[Prime[n]^n, {n,20}] (* Harvey P. Dale, Jun 22 2011 *)

a(n) = prime(n)^n; \\ Harry J. Smith, Aug 07 2009

a(n) = A062006(n) - 1. - Wesley Ivan Hurt, Jan 18 2016
From Amiram Eldar, Nov 16 2020: (Start)
Sum_{n>=1} 1/a(n) = A093358.
Sum_{n>=1} (-1)^(n+1)/a(n) = A201614. (End)

A201614 Decimal expansion of Sum_{n = 1 .. infinity } (-1)^(n+1)/ prime(n)^n.

Original entry on oeis.org

3, 9, 6, 4, 7, 8, 4, 0, 0, 1, 7, 6, 7, 2, 8, 8, 0, 1, 3, 2, 0, 3, 7, 7, 2, 1, 9, 5, 4, 9, 1, 4, 5, 0, 1, 3, 1, 1, 7, 8, 3, 7, 6, 1, 4, 2, 2, 1, 9, 0, 4, 1, 8, 5, 1, 5, 8, 6, 6, 3, 8, 8, 9, 5, 4, 4, 0, 1, 0, 8, 7, 8, 0, 8, 5, 0, 8, 7, 7, 9, 9, 7, 0, 3, 9, 5, 5, 5, 9, 1, 1, 1, 0, 5, 2, 9, 9, 2, 9, 0, 2, 5, 5, 9, 8

Offset: 0

Michel Lagneau, Dec 03 2011

			0.39647840017672880132037721... = 1/2^1 - 1/3^2 + 1/5^3 - 1/7^4 + ...

Cf. A062457, A093358.

with(numtheory): Digits:=105:s:=sum( evalf(((-1)^(n+1))/ ithprime(n)^n),n=1..200):print(s):

digits = 105; NSum[(-1)^(n+1)/Prime[n//Round]^n, {n, 1, Infinity},  Method -> "AlternatingSigns", WorkingPrecision -> digits, NSumTerms -> digits] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 24 2014 *)

cp's OEIS Frontend

A062457 a(n) = prime(n)^n.

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