A291192 Squarefree composite numbers n such that n*sigma(n) is of the form k*(k+1).

6, 42, 1430, 3686, 5685, 23815, 60235, 129778, 370991, 652289, 654545, 660265, 795405, 801645, 1532170, 3413267, 3457597, 4235270, 4282330, 8107937, 9679187, 10835013, 15464685, 15963578, 16636503, 24976497, 28122458, 29595310, 34759879, 35642479, 58525286

Offset

1,1

Comments

Also squarefree composite numbers n such that Product_{p|n, p prime} A002378(p) is in A002378.

Is this sequence infinite?

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..63

Example

42 = 2*3*7 is a term because 42*sigma(42) = 42(2+1)(3+1)(7+1) = 4032 = 63*64.

Mathematica

Select[Range[586*10^5], CompositeQ[#]&&SquareFreeQ[#]&&OddQ[Sqrt[1+4(# DivisorSigma[ 1, #])]]&] (* Harvey P. Dale, Nov 23 2023 *)

Prog

(PARI) is(n, f=factor(n))=#f~>1 && vecmax(f[, 2])==1 && ispolygonal(n*sigma(f)/2, 3)
list(lim)=my(v=List()); forfactored(n=6, lim\1, if(call(is, n), listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Aug 22 2017

Crossrefs

Cf. A002378, A064987.

Sequence in context: A330345 A273922 A139223 * A185222 A179861 A083940

Adjacent sequences: A291189 A291190 A291191 * A291193 A291194 A291195

Keyword

nonn

Author

Altug Alkan and Thomas Ordowski, Aug 20 2017

Status

approved