A074736 Goedel encoding of the prime factors of n, in increasing order and repeated according to multiplicity.

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

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)[1], 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