login
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
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
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)[1], for(l=1, m[k, 2], s=s*prime(c)^m[k, 1]:c=c+1)):print1(s", "))
CROSSREFS
Sequence in context: A266676 A046056 A158863 * A044829 A338086 A033001
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Sep 28 2002
EXTENSIONS
More terms from Ralf Stephan, Mar 22 2003
STATUS
approved