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A054412
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Numbers n such that, in the prime factorization of n, the product of exponents equals the product of prime factors.
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14
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1, 4, 27, 72, 108, 192, 800, 1458, 3125, 5120, 6272, 12500, 21600, 30375, 36000, 48600, 77760, 84375, 114688, 116640, 121500, 138240, 169344, 225000, 247808, 337500, 384000, 395136, 600000, 653184, 750141, 823543, 857304, 979776, 1384448, 1474560, 1500000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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For p prime, numbers of the form p^p satisfy the condition, hence A051674 is a subsequence. - Michel Marcus, May 19 2014
Also, numbers of the form p^q * q^p, with distinct primes p and q, satisfy the condition, hence A082949 is a subsequence. - Bernard Schott, Apr 11 2020
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LINKS
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EXAMPLE
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192 is included because 192 =2^6 *3^1 and 2*3 = 6*1.
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MATHEMATICA
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peppfQ[n_]:=Module[{f=Transpose[FactorInteger[n]]}, Times@@First[f] == Times@@Last[f]]; Select[Range[1.5*10^6], peppfQ] (* Harvey P. Dale, Oct 14 2015 *)
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PROG
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(PARI) isok(n) = my(f = factor(n)); prod(i=1, #f~, f[i, 2]) == prod(i=1, #f~, f[i, 1]); \\ Michel Marcus, May 19 2014
(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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