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Search: id:A071364
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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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+0
12
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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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}] (*Chandler*)
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CROSSREFS
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Cf. A071365, A071366.
Sequence in context: A119655 A083260 A046523 this_sequence A067824 A107067 A046801
Adjacent sequences: A071361 A071362 A071363 this_sequence A071365 A071366 A071367
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 21 2002
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 23 2005
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