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A323129
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a(1) = 1, and for any n > 1, let p be the greatest prime factor of n, and e be its exponent, then a(n) = p^a(e).
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2
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1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 9, 19, 5, 7, 11, 23, 3, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 49, 25, 17, 13, 53, 27, 11, 7, 19, 29, 59, 5, 61, 31, 7, 8, 13, 11, 67, 17, 23, 7, 71, 9, 73
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OFFSET
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1,2
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COMMENTS
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This sequence is a recursive variant of A053585.
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LINKS
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FORMULA
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a(n) <= n with equality iff n belongs to A164336.
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EXAMPLE
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a(1458) = a(2 * 3^6) = 3^a(6) = 3^a(2*3) = 3^3 = 27.
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MAPLE
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f:= proc(n) option remember;
local F, t;
F:= ifactors(n)[2];
t:= F[max[index](map(t -> t[1], F))];
t[1]^procname(t[2]);
end proc:
f(1):= 1:
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MATHEMATICA
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Nest[Append[#, Last@ FactorInteger[Length[#] + 1] /. {p_, e_} :> p^#[[e]] ] &, {1}, 72] (* Michael De Vlieger, Jan 07 2019 *)
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PROG
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(PARI) a(n) = if (n==1, 1, my (f=factor(n)); f[#f~, 1]^a(f[#f~, 2]))
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CROSSREFS
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See A323130 for the variant involving the least prime factor.
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KEYWORD
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AUTHOR
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STATUS
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approved
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