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A025487
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List giving least integer of each prime signature; also products of primorial numbers A002110.
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225
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1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, 240, 256, 288, 360, 384, 420, 432, 480, 512, 576, 720, 768, 840, 864, 900, 960, 1024, 1080, 1152, 1260, 1296, 1440, 1536, 1680, 1728, 1800, 1920, 2048, 2160, 2304, 2310
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All numbers of the form 2^k1*3^k2*...*p_n^k_n, where k1 >= k2 >= ... >= k_n, sorted.
A111059 is a subsequence. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 05 2010]
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REFERENCES
| The exponents k1, k2, ... can be read off Abramowitz and Stegun, Handbook, p. 831, column labeled "pi".
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LINKS
| Will Nicholes and Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10001 (Will Nicholes supplied the first 291 terms.)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
| What can be said about the asymptotic behavior of this sequence? - Franklin T. Adams-Watters, Jan 06 2010
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EXAMPLE
| The first few terms are 1, 2, 2^2, 2*3, 2^3, 2^2*3, 2^4, 2^3*3, 2*3*5, ...
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MATHEMATICA
| PrimeExponents[n_] := Last /@ FactorInteger[n]; lpe = {}; ln = {1}; Do[pe = Sort@PrimeExponents@n; If[ FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]], {n, 2, 2350}]; ln (* Robert G. Wilson v, Aug 14 2004 *)
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PROG
| (PARI) isA025487(n)=my(k=valuation(n, 2), t); n>>=k; forprime(p=3, default(primelimit), t=valuation(n, p); if(t>k, return(0), k=t); if(k, n/=p^k, return(n==1))) \\ Charles R Greathouse IV, Jun 10 2011
(PARI) factfollow(n)={local(fm, np, n2);
fm=factor(n); np=matsize(fm)[1];
if(np==0, return([2]));
n2=n*nextprime(fm[np, 1]+1);
if(np==1||fm[np, 2]<fm[np-1, 2], [n*fm[np, 1], n2], [n2])}
al(n) = {local(r, ms); r=vector(n);
ms=[1];
for(k=1, n,
r[k]=ms[1];
ms=vecsort(concat(vector(#ms-1, j, ms[j+1]), factfollow(ms[1]))));
r} /* Franklin T. Adams-Watters, Dec 01 2011 */
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CROSSREFS
| Cf. A001013, A036035, A025488, A051282, A055932, A036041, A061394, A124832.
Equals range of values taken by A046523.
Sequence in context: A048951 A058629 A095810 * A070175 A096850 A062847
Adjacent sequences: A025484 A025485 A025486 * A025488 A025489 A025490
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Offset corrected by Matthew Vandermast (ghodges14(AT)comcast.net), Oct 19 2008
Minor correction by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 03 2010
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