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 A071364 Smallest number with same sequence of exponents in canonical prime factorization as n. 26
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS Daniel Forgues, Table of n, a(n) for n=1..100000 FORMULA 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 EXAMPLE a(105875) = a(5*5*5*7*11*11) = 2*2*2*3*5*5 = 600. MATHEMATICA Table[ e = Last /@ FactorInteger[n]; Product[Prime[i]^e[[i]], {i, Length[e]}], {n, 88}] (* Ray Chandler, Sep 23 2005 *) PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 21 2002 EXTENSIONS Extended by Ray Chandler, Sep 23 2005 STATUS approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)