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A231231 Numbers n such that, in the prime factorization of n, the product of the exponents equals the sum of prime factors and exponents. 1
432, 648, 1152, 4000, 5400, 8748, 9000, 12800, 12960, 13500, 17280, 19440, 21952, 25000, 48000, 48384, 50625, 60000, 78400, 87480, 100352, 114048, 150000, 189000, 202176, 263424, 303264, 303750, 304128, 340736, 356400, 367416, 368640, 370440, 374544, 384912 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n = p_1^c_1 * p_2^c_2 * p_3^c_3 * ... * p_k^c_k, where c's are positive integers and p's are distinct primes, then product{j=1 to k}[c_j] = sum{j=1 to k}[p_j+c_j].

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

9000 = 3^2 * 2^3 * 5^3. Product of exponents is 2*3*3=18, sum of prime factors and exponents is 3+2+2+3+5+3=18, hence 9000 is in the sequence.

MATHEMATICA

t = {}; n = 1; While[Length[t] < 38, n++; f = FactorInteger[n]; sm = Total[Flatten[f]]; pr = Times @@ Transpose[f][[2]]; If[sm == pr, AppendTo[t, n]]]; t (* T. D. Noe, Nov 08 2013 *)

CROSSREFS

Cf. A054411, A054412, A071174, A071175, A122406, A231293.

Sequence in context: A066419 A245469 A069781 * A179666 A203663 A250815

Adjacent sequences:  A231228 A231229 A231230 * A231232 A231233 A231234

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Nov 06 2013

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)