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A054412
Numbers n such that, in the prime factorization of n, the product of exponents equals the product of prime factors.
14
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
OFFSET
1,2
COMMENTS
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
LINKS
EXAMPLE
192 is included because 192 =2^6 *3^1 and 2*3 = 6*1.
MATHEMATICA
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 *)
PROG
(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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, May 09 2000
EXTENSIONS
More terms from James A. Sellers, May 23 2000
New name and three more terms from Michel Marcus, May 19 2014
STATUS
approved