A167657 - OEIS

%I #20 Sep 08 2022 08:45:48

%S 0,1,4,9,256,25,1296,49,4096,531441,100,1771561,20736,169,38416,

%T 11390625,16777216,289,34012224,130321,400,85766121,234256,148035889,

%U 110075314176,390625,676,531441,784,707281,478296900000000000000,923521

%N Product of n-th block of identical consecutive values of A000720.

%H Jason Kimberley, <a href="/A167657/b167657.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n^(A000040(n+1)-A000040(n)). - _Jason Kimberley_, May 27 2018

%p 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

%t Most@ Map[Times @@ # &, Split@ Array[PrimePi, 132]] (* _Michael De Vlieger_, May 27 2018 *)

%o (Magma) A40:=NthPrime;

%o A167657:=func<n|(n-1)^(A40(n)-A40(n-1))>;

%o [A167657(n):n in[1..32]]; // _Jason Kimberley_, May 27 2018

%Y Cf. A000720.

%K nonn,look

%O 1,3

%A _Giovanni Teofilatto_, Nov 08 2009

%E a(1) = 0 and a(5) = 256 corrected by _Giovanni Teofilatto_, Nov 12 2009

%E a(17) inserted and a(20) corrected by _R. J. Mathar_, Jan 30 2010

%E Name edited by _Jason Kimberley_, Jul 01 2018