A071364 - OEIS

A071364

Smallest number with same sequence of exponents in canonical prime factorization as n.

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

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)