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A284262
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a(n) = where A284259 for the first time obtains value n (positions of its records).
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3
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1, 2, 6, 105, 5005, 85085, 1616615, 37182145, 6685349671, 247357937827, 10141675450907, 436092044389001, 20496326086283047, 9156001667401012567, 558516101711461766587, 37420578814667938361329, 2656861095841423623654359, 193950859996423924526768207, 15322117939717490037614688353, 1271735788996551673122019133299
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OFFSET
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0,2
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LINKS
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FORMULA
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For n > 1, a(n) = Product_{i = A284263(n)+1 .. A284263(n)+n} prime(i); a(0) = 1, a(1) = 2.
Other identities. For all n >= 0:
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MATHEMATICA
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A[n_]:= If[n<1, 0, Block[{k=1}, While[Prime[n + k - 1] > Prime[k]^2, k++]; k - 1]]; a[n_]:=If[n<2, n + 1, Product[Prime[i], {i, A[n] + 1, A[n] + n}]]; Table[a[n], {n, 0, 51}] (* Indranil Ghosh, Mar 24 2017 *)
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PROG
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(PARI) A(n) = { my(k=1); if(0==n, 0, while(prime(n+k-1) > (prime(k)^2), k = k+1); (k-1)); };
a(n) = prod(i=A(n) + 1, A(n) + n, prime(i));
(Python)
from sympy import prime
from operator import mul
from functools import reduce
def A(n):
if n<1: return 0
k=1
while prime(n + k - 1)>prime(k)**2:k+=1
return k - 1
def a(n): return n + 1 if n<2 else reduce(mul, [prime(i) for i in range(A(n) + 1, A(n) + n + 1)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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