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A071364
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Smallest number with same sequence of exponents in canonical prime factorization as n.
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28
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1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 12, 2, 6, 6, 16, 2, 18, 2, 12, 6, 6, 2, 24, 4, 6, 8, 12, 2, 30, 2, 32, 6, 6, 6, 36, 2, 6, 6, 24, 2, 30, 2, 12, 12, 6, 2, 48, 4, 18, 6, 12, 2, 54, 6, 24, 6, 6, 2, 60, 2, 6, 12, 64, 6, 30, 2, 12, 6, 30, 2, 72, 2, 6, 18, 12, 6, 30, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24
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OFFSET
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1,2
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COMMENTS
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a(a(n))=a(n); a(n)=2^k iff n=p^k, p prime, k>0 (A000961); if n>1 is not a prime power, then a(n) mod 6 = 0; range of values = A055932, as distinct prime factors of a(n) are consecutive: a(n)=n iff n=A055932(k) for some k;
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LINKS
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FORMULA
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In prime factorization of n, replace least prime by 2, next least by 3, etc.
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EXAMPLE
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a(105875) = a(5*5*5*7*11*11) = 2*2*2*3*5*5 = 600.
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MATHEMATICA
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Table[ e = Last /@ FactorInteger[n]; Product[Prime[i]^e[[i]], {i, Length[e]}], {n, 88}] (* Ray Chandler, Sep 23 2005 *)
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PROG
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(Haskell)
a071364 = product . zipWith (^) a000040_list . a124010_row
(PARI) a(n) = f = factor(n); for (i=1, #f~, f[i, 1] = prime(i)); factorback(f); \\ Michel Marcus, Jun 13 2014
(Python)
from math import prod
from sympy import prime, factorint
def A071364(n): return prod(prime(i+1)**p[1] for i, p in enumerate(sorted(factorint(n).items()))) # Chai Wah Wu, Sep 16 2022
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CROSSREFS
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Unsorted prime signature is A124010.
Numbers whose prime signature is aperiodic are A329139.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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