A340834 Fixed points of A341885.

12, 1222, 1437286, 3441373, 1032893366969

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 22 2021

Keywords

• nonn
• more

Comments

Numbers n such that A341885(n) = n.

Includes 2*p*q if p and q are primes such that p^2-4*p*q+q^2+p+q+6 = 0. This includes 12 for p=2, q=3, 1222 for p=13,q=47, 1437286 for p=439, q=1637, and 76498942675946443126 for p=3201392659, q=11947760057.

Another term: 6538810199342921107066977217325653068509 = 13 * 4401624135264074597*114272683103433355069. - Chai Wah Wu, Feb 25 2021

Examples

			a(2) = 1222 is a term because 1222 = 2*13*47 and A341885(1222) = 2*3/2 + 13*14/2 + 47*48/2 = 1222.
		

Crossrefs

Cf. A341885.

Programs

Maple

f:= proc(n) local F,t;
  F:= ifactors(n)[2];
  add(t[1]*(t[1]+1)/2*t[2],t=F)
end proc:
select(t -> f(t)=t, [$1..4000000]);

Mathematica

Block[{a = {}}, Monitor[Do[If[# == i, AppendTo[a, i]] &@ Total[PolygonalNumber@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[i]]], {i, 2, 4*10^6}], i]; a] (* Michael De Vlieger, Feb 22 2021 *)

Python

from sympy import factorint
A340834_list = [n for n in range(2,10**4) if n == sum(k*m*(m+1)//2 for m,k in factorint(n).items())] # Chai Wah Wu, Feb 25 2021

Formula

A341885(a(n)) = a(n).

Extensions

a(5) from Martin Ehrenstein, Mar 07 2021