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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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26
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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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A046523(a(n))=A046523(n); A046523(n)<=a(n)<=n; A001221(a(n))=A001221(n), A001222(a(n))=A001222(n); A020639(a(n))=2, A006530(a(n))=A000040(A001221(n))<=A006530(n); A000005(a(n))=A000005(n);
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;
a(A003586(n))=A003586(n).
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LINKS
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Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
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In prime factorization of n, replace least prime by 2, next least by 3, etc.
a(n) = product(A000040(k)^A124010(k): k=1..A001221(n)). - Reinhard Zumkeller, Apr 27 2013
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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
-- Reinhard Zumkeller, Feb 19 2012
(PARI) a(n) = f = factor(n); for (i=1, #f~, f[i, 1] = prime(i)); factorback(f); \\ Michel Marcus, Jun 13 2014
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CROSSREFS
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Cf. A071365, A071366.
Cf. A000040.
Cf. A085079, A089247.
The range is A055932.
The reversed version is A331580.
Unsorted prime signature is A124010.
Numbers whose prime signature is aperiodic are A329139.
Cf. A056239, A112798, A233249, A333217, A333219, A334032, A334033.
Sequence in context: A046523 A278524 A278523 * A278237 A328707 A067824
Adjacent sequences: A071361 A071362 A071363 * A071365 A071366 A071367
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 21 2002
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EXTENSIONS
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Extended by Ray Chandler, Sep 23 2005
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STATUS
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approved
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