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1, 2, 6, 3, 30, 5, 210, 6, 15, 7, 2310, 10, 30030, 11, 21, 5, 510510, 30, 9699690, 14, 33, 13, 223092870, 15, 105, 17, 14, 22, 6469693230, 42, 200560490130, 10, 39, 19, 165, 7, 7420738134810, 23, 51, 21, 304250263527210, 66, 13082761331670030, 26, 70, 29, 614889782588491410, 30, 1155, 210, 57, 34, 32589158477190044730, 21, 195, 33, 69, 31
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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Other identities:
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MATHEMATICA
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Table[FixedPoint[Times @@ Map[#1^#2 & @@ # &, Partition[#, 2, 2] &@ Flatten[FactorInteger[#] /. {p_, e_} /; e >= 2 :> {If[OddQ@ e, {p, 1}, {1, 1}], {NextPrime@ p, Floor[e/2]}}]] &, #] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[n] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]], {n, 58}] (* Michael De Vlieger, Mar 18 2017 *)
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PROG
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(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };
(Python)
from sympy import primerange, factorint, nextprime
from operator import mul
def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
def a108951(n):
f = factorint(n)
return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])
def a097246(n):
f=factorint(n)
return 1 if n==1 else reduce(mul, [(nextprime(i)**int(f[i]/2))*(i**(f[i]%2)) for i in f])
def a097248(n):
k=a097246(n)
while k!=n:
n=k
k=a097246(k)
return k
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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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