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 A046523 Smallest number with same prime signature as n. 412
 1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 12, 2, 6, 6, 16, 2, 12, 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, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 60, 2, 6, 12, 64, 6, 30, 2, 12, 6, 30, 2, 72, 2, 6, 12, 12, 6, 30, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA In prime factorization of n, replace most common prime by 2, next most common by 3, etc. a(n) = A124859(A124859(n)) = A181822(A124859(n)). - Matthew Vandermast, May 19 2012 a(n) = A181821(A181819(n)). - Alois P. Heinz, Feb 17 2020 EXAMPLE If p,q,... are different primes, a(p)=2, a(p^2)=4, a(pq)=6, a(p^2*q)=12, etc. n = 108 = 2*2*3*3*3 is replaced by a(n) = 2*2*2*3*3 = 72; n = 105875 = 5*5*5*7*11*11 is represented by a(n) = 2*2*2*3*3*5 = 360. Prime-powers are replaced by corresponding powers of 2, primes by 2. Factorials, primorials and lcm[1..n] are in the sequence. A000005(a(n)) = A000005(n) remains invariant; least and largest prime factors of a(n) are 2 or p[A001221(n)] resp. MAPLE a:= n-> (l-> mul(ithprime(i)^l[i], i=1..nops(l)))         (sort(ifactors(n), (x, y)->x>y)): seq(a(n), n=1..100);  # Alois P. Heinz, Aug 18 2014 MATHEMATICA Table[Apply[Times, p[w]^Reverse[Sort[ex[w]]]], {w, 1, 1000}] p[x_] := Table[Prime[w], {w, 1, lf[x]}] ex[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ps[n_] := Sort[Last /@ FactorInteger[n]]; Join[{1}, Table[i = 2; While[ps[n] != ps[i], i++]; i, {n, 2, 89}]] (* Jayanta Basu, Jun 27 2013 *) PROG (PARI) a(n)=my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ Charles R Greathouse IV, Aug 17 2011 (PARI) A046523(n)=factorback(primes(#n=vecsort(factor(n)[, 2], , 4)), n) \\ M. F. Hasler, Oct 12 2018, improved Jul 18 2019 (Haskell) import Data.List (sort) a046523 = product .           zipWith (^) a000040_list . reverse . sort . a124010_row -- Reinhard Zumkeller, Apr 27 2013 (Python) from sympy import factorint def P(n):     f = factorint(n)     return sorted([f[i] for i in f]) def a(n):     x=1     while True:         if P(n) == P(x): return x         else: x+=1 # Indranil Ghosh, May 05 2017 CROSSREFS A025487 gives range of values of this sequence. Cf. A000142, A002110, A003418, A001221, A000040, A000005, A124010, A071364, A085079, A089247. Cf. A181819, A181821. Sequence in context: A083260 A284011 A275468 * A278524 A278523 A071364 Adjacent sequences:  A046520 A046521 A046522 * A046524 A046525 A046526 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Corrected and extended by Ray Chandler, Mar 11 2004 STATUS approved

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Last modified September 18 20:19 EDT 2020. Contains 337173 sequences. (Running on oeis4.)