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A064549
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a(n) = n * Product_{primes p|n} p.
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6
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1, 4, 9, 8, 25, 36, 49, 16, 27, 100, 121, 72, 169, 196, 225, 32, 289, 108, 361, 200, 441, 484, 529, 144, 125, 676, 81, 392, 841, 900, 961, 64, 1089, 1156, 1225, 216, 1369, 1444, 1521, 400, 1681, 1764, 1849, 968, 675, 2116, 2209, 288, 343, 500, 2601, 1352
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Multiplicative with a(p^k)=p^(k+1) when k>0.
a(n) = n*A007947(n) = n^2/A003557(n).
Dirichlet convolution of A000027 and A202535. - R. J. Mathar, Dec 20 2011
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EXAMPLE
| a(12)=72 since 12=2^2*3 and 12*2*3 = 72.
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PROG
| (PARI) popf(n)= { local(f, p=1); f=factor(n); for(i=1, matsize(f)[1], p*=f[i, 1]); return(p) } { for (n=1, 1000, write("b064549.txt", n, " ", n*popf(n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 18 2009]
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CROSSREFS
| A permutation of the powerful numbers A001694.
Sequence in context: A050399 A072995 A073395 * A087687 A168175 A164382
Adjacent sequences: A064546 A064547 A064548 * A064550 A064551 A064552
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KEYWORD
| mult,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 16 2001
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