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Integer part of 4th root of product of first n primes.
5

%I #33 Nov 28 2021 03:07:32

%S 1,1,1,2,3,6,13,26,55,122,283,669,1650,4176,10694,28002,75555,209402,

%T 585212,1674296,4860120,14206194,42353033,127836257,392646335,

%U 1232237672,3906383039,12444691408,40024883480,129326254765

%N Integer part of 4th root of product of first n primes.

%C For n>=6, a(n) >= prime(n+1).

%C a(n) gives the number of pairs within A002110(n) of the form {x, x^4} where x is nonzero positive integer. - _Soumyadeep Dhar_, May 16 2021

%H Soumyadeep Dhar, <a href="/A127601/b127601.txt">Table of n, a(n) for n = 0..1154</a>

%t a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/4)]], {n, 1, 50}]; a

%o (PARI) a(n)={sqrtnint(vecprod(primes(n)), 4)} \\ _Andrew Howroyd_, Apr 27 2021

%Y Cf. A002110, A060797, A127600, A127602, A127603, A127604.

%K nonn

%O 0,4

%A _Artur Jasinski_, Jan 19 2007

%E a(0)=1 prepended by _Soumyadeep Dhar_, Apr 28 2021