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A340834 Fixed points of A341885. 1
12, 1222, 1437286, 3441373, 1032893366969 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..5.

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

Cf. A341885.

Sequence in context: A301474 A054351 A080814 * A078294 A317953 A009155

Adjacent sequences:  A340831 A340832 A340833 * A340835 A340836 A340837

KEYWORD

nonn,more

AUTHOR

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

EXTENSIONS

a(5) from Martin Ehrenstein, Mar 07 2021

STATUS

approved

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Last modified May 15 22:33 EDT 2021. Contains 343937 sequences. (Running on oeis4.)