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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. 13
 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)
 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 Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A054412 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 Cf. A051674, A054411, A082949. Sequence in context: A272858 A272818 A272859 * A122405 A122406 A276372 Adjacent sequences:  A054409 A054410 A054411 * A054413 A054414 A054415 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

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)