A167657 Product of n-th block of identical consecutive values of A000720.

0, 1, 4, 9, 256, 25, 1296, 49, 4096, 531441, 100, 1771561, 20736, 169, 38416, 11390625, 16777216, 289, 34012224, 130321, 400, 85766121, 234256, 148035889, 110075314176, 390625, 676, 531441, 784, 707281, 478296900000000000000, 923521

Offset: 1

Author

Giovanni Teofilatto, Nov 08 2009

Keywords

• nonn
• look

Links

• Jason Kimberley, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720.

Programs

Magma

A40:=NthPrime;
A167657:=func;
[A167657(n):n in[1..32]]; // Jason Kimberley, May 27 2018

Maple

A000720 := proc(n) numtheory[pi](n) ; end proc: A167657 := proc(nmax) local ol,a ; ol := 0 ; a := 0 ; for n from 1 to nmax do if A000720(n) = ol then a := a*ol ; else printf("%d,",a) ; a := A000720(n) ; end if; ol := A000720(n) ; end do ; return ; end proc: A167657(160) ; # R. J. Mathar, Jan 30 2010

Mathematica

Most@ Map[Times @@ # &, Split@ Array[PrimePi, 132]] (* Michael De Vlieger, May 27 2018 *)

Formula

a(n) = n^(A000040(n+1)-A000040(n)). - Jason Kimberley, May 27 2018

Extensions

a(1) = 0 and a(5) = 256 corrected by Giovanni Teofilatto, Nov 12 2009

a(17) inserted and a(20) corrected by R. J. Mathar, Jan 30 2010

Name edited by Jason Kimberley, Jul 01 2018