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A219964
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a(n) = product(i >= 0, (P(n, i)/P(n-1, i))^(2^i)) where P(n, i) = product(p prime, n/2^(i+1) < p <= n/2^i).
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2
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1, 1, 2, 3, 2, 5, 3, 7, 4, 1, 5, 11, 9, 13, 7, 1, 16, 17, 1, 19, 25, 1, 11, 23, 81, 1, 13, 1, 49, 29, 1, 31, 256, 1, 17, 1, 1, 37, 19, 1, 625, 41, 1, 43, 121, 1, 23, 47, 6561, 1, 1, 1, 169, 53, 1, 1, 2401, 1, 29, 59, 1, 61, 31, 1, 65536, 1, 1, 67, 289, 1, 1, 71
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OFFSET
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0,3
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COMMENTS
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If n > 0 then a(n) = 1 if and only if n is an element of A110473.
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LINKS
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FORMULA
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EXAMPLE
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a(20) = (7/(5*7))^2*((3*5)/3)^4 = 25.
a(22) = ((13*17*19)/(11*13*17*19))*((7*11)/7)^2 = 11.
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MAPLE
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if isprime(n) then RETURN(n) fi;
z := 1; l := n - 1; m := n;
do l := iquo(l, 2); m := iquo(m, 2);
if l = 0 then break fi;
if l < m then if isprime(l+1) then RETURN((l+1)^z) fi fi;
z := z + z;
od; 1 end: seq(A219964(k), k=0..71);
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MATHEMATICA
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a[n_] := Module[{l, m, z}, If[PrimeQ[n] , Return[n] ]; z = 1; l = Max[0, n - 1]; m = n; While[True, l = Quotient[l, 2]; m = Quotient[m, 2]; If[l == 0 , Break[]]; If[l < m , If[ PrimeQ[l+1], Return[(l+1)^z]]]; z = z+z]; 1]; Table[a[k], {k, 0, 71}] (* Jean-François Alcover, Jan 15 2014, after Maple *)
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PROG
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(J)
genSeq=: 3 :0
p=. x: i.&.(_1&p:) y1=.y+1
i=.(#~y1>])&.> <:@((i.@>.&.(2&^.)y1)*])&.> p
y{.(; p(^2x^0, i.@<:@#)&.>i) (; i) } y1$1
)
(Sage)
if is_prime(n): return n
z = 1; l = max(0, n-1); m = n
while true:
l = l // 2
m = m // 2
if l == 0: break
if l < m:
if is_prime(l+1): return (l+1)^z
z = z + z
return 1
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CROSSREFS
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Cf. A220027, the partial products of a(n).
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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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