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 A074736 Goedel encoding of the prime factors of n, in increasing order and repeated according to multiplicity. 3
 4, 8, 36, 32, 108, 128, 900, 216, 972, 2048, 4500, 8192, 8748, 1944, 44100, 131072, 13500, 524288, 112500, 17496, 708588, 8388608, 308700, 7776, 6377292, 27000, 2812500, 536870912, 337500, 2147483648, 5336100, 1417176, 516560652, 69984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For irregular triangle T(n,k) at A027746, a(n) = Product_{1..A001222(n)} pi(k)^T(n,k). - Michael De Vlieger, May 04 2020. REFERENCES K. Gödel, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems", Dover Publications, 1992. LINKS Michael De Vlieger, Table of n, a(n) for n = 2..3322 FORMULA a(n) = prime(1)^p_1 * prime(2)^p_2 * ... * prime(k)^p_k, where p_1 <= ... <= p_k are the prime factors of n, repeated according to multiplicity. EXAMPLE The prime factors of 12 in increasing order and repeated according to multiplicity are 2, 2, 3. Hence a(12) = 2^2 * 3^2 * 5^3 = 4500. MATHEMATICA Array[Times @@ MapIndexed[Prime[First[#2]]^#1 &, Apply[Join, ConstantArray[#1, #2] & @@@ FactorInteger[#]]] &, 34, 2] (* Michael De Vlieger, May 04 2020 *) PROG (PARI) for(n=2, 50, m=factor(n):s=1:c=1:for(k=1, matsize(m), for(l=1, m[k, 2], s=s*prime(c)^m[k, 1]:c=c+1)):print1(s", ")) CROSSREFS Cf. A001222, A027746. Sequence in context: A266676 A046056 A158863 * A044829 A338086 A033001 Adjacent sequences:  A074733 A074734 A074735 * A074737 A074738 A074739 KEYWORD nonn AUTHOR Joseph L. Pe, Sep 28 2002 EXTENSIONS More terms from Ralf Stephan, Mar 22 2003 STATUS approved

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Last modified September 27 07:56 EDT 2022. Contains 357052 sequences. (Running on oeis4.)