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A124859
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Multiplicative with p^e -> primorial(e), p prime and e > 0.
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15
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1, 2, 2, 6, 2, 4, 2, 30, 6, 4, 2, 12, 2, 4, 4, 210, 2, 12, 2, 12, 4, 4, 2, 60, 6, 4, 30, 12, 2, 8, 2, 2310, 4, 4, 4, 36, 2, 4, 4, 60, 2, 8, 2, 12, 12, 4, 2, 420, 6, 12, 4, 12, 2, 60, 4, 60, 4, 4, 2, 24, 2, 4, 12, 30030, 4, 8, 2, 12, 4, 8, 2, 180, 2, 4, 12, 12, 4, 8, 2, 420, 210, 4, 2, 24, 4, 4
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Primorial
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FORMULA
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(End)
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EXAMPLE
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a(2) = 2 since 2 = 2^1, thus primorial p_1# = 2.
a(4) = 6 since 4 = 2^2, thus primorial p_2# = 2*3 = 6.
a(6) = 4 because 6 is squarefree with omega(6)=2, thus 2^2 = 4.
a(8) = 30 since 8 = 2^3, thus primorial p_3# = 2*3*5 = 30.
a(10) = 4 since 10 is squarefree with omega(10)=2, thus 2^2 = 4.
a(12) = 12 since 12 = 2^1 * 3^2, thus primorials p_1# * p_2# = 2*6 = 12.
(End)
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MAPLE
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local a, pf;
a := 1;
for pf in ifactors(n)[2] do
end do:
a ;
end proc:
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MATHEMATICA
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Table[Which[n == 1, 1, SquareFreeQ@ n, 2^PrimeNu@ n, True, Times @@ Map[Times @@ Prime@ Range@ # &, #[[All, -1]]]] &@ FactorInteger@ n, {n, 86}] (* Michael De Vlieger, Mar 06 2017 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 16 2015
(Python)
from sympy.ntheory.factor_ import core
from sympy import factorint, primorial, primefactors
from operator import mul
def omega(n): return 0 if n==1 else len(primefactors(n))
def a(n):
f=factorint(n)
return n if n<3 else 2**omega(n) if core(n) == n else reduce(mul, [primorial(f[i]) for i in f]) # Indranil Ghosh, May 13 2017
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CROSSREFS
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Cf. A000040, A000079, A001221, A001222, A002110, A005117, A028234, A046523, A067029, A072048, A108951, A156552, A181819, A181821, A238745, A278159, A278222.
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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