OFFSET
1,1
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
FORMULA
A341885(a(n)) = a(n).
EXAMPLE
a(2) = 1222 is a term because 1222 = 2*13*47 and A341885(1222) = 2*3/2 + 13*14/2 + 47*48/2 = 1222.
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 *)
PROG
(Python3)
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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Feb 22 2021
EXTENSIONS
a(5) from Martin Ehrenstein, Mar 07 2021
STATUS
approved