A062457 - OEIS

%I #54 Oct 09 2022 10:34:39

%S 2,9,125,2401,161051,4826809,410338673,16983563041,1801152661463,

%T 420707233300201,25408476896404831,6582952005840035281,

%U 925103102315013629321,73885357344138503765449,12063348350820368238715343,3876269050118516845397872321

%N a(n) = prime(n)^n.

%C 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

%C Main diagonal of A182944. - _Omar E. Pol_, Sep 12 2018

%C Second diagonal of A319075. - _Omar E. Pol_, Sep 13 2018

%H T. D. Noe, <a href="/A062457/b062457.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = A062006(n) - 1. - _Wesley Ivan Hurt_, Jan 18 2016

%F From _Amiram Eldar_, Nov 16 2020: (Start)

%F Sum_{n>=1} 1/a(n) = A093358.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = A201614. (End)

%p A062457:=n->ithprime(n)^n: seq(A062457(n), n=1..20); # _Wesley Ivan Hurt_, Jan 18 2016

%t Table[Prime[n]^n, {n,20}] (* _Harvey P. Dale_, Jun 22 2011 *)

%o (PARI) a(n) = prime(n)^n; \\ _Harry J. Smith_, Aug 07 2009

%o (Magma) [NthPrime(n)^n : n in [1..20]]; // _Wesley Ivan Hurt_, Jan 18 2016

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

%K easy,nonn

%O 1,1

%A _Labos Elemer_, Jul 09 2001