A194080 Partial sums of the squarefree integers that are triangular.

1, 3, 6, 45, 2775, 239778, 3293461, 3815703, 8142176137578, 25025955346953, 27262684236385, 2430563686654005, 17543349622599580, 95966329187365806, 69152680331115315990, 130831703828369011153, 10553338813847920825078, 120456843371021570368956

Offset: 1

Author

Robert G. Wilson v, Aug 19 2011

Keywords

• nonn

Comments

For the partial sum to the squarefree integer: 1, 2, 3, 11, 94, 890, 3290, 3538, 5175587, 9073717, 9470490, 89421695, 240240143, ..., .

No more terms in the first 4*10^11 partial sums. - Donovan Johnson, Feb 20 2012

Crossrefs

Cf. A005117, A173143.

Programs

Mathematica

triQ[n_] := IntegerQ@ Sqrt[ 8n + 1]; k = 1; s = 0; lst = {}; While[k < 3*10^8, If[ SquareFreeQ@ k, s = s + k; If[ triQ@ s, AppendTo[lst, s]; Print[{k, s}]]]; k++]

Extensions

a(14)-a(16) from Donovan Johnson, Aug 24 2011

a(17)-a(18) from Donovan Johnson, Feb 20 2012