A329328 The squares in A329472.

4, 49, 1024, 11881, 15876, 29241, 23530332816, 90070213689, 165698657721, 233002186209, 8246098046404, 363533405168704, 24015392820628036, 48563553937960000, 6648251155785800089, 497199122464645742436, 749745222626569665409, 10925409774976373110009

Offset

1,1

Comments

The first 18 terms are the sums of the first 1, 5, 27, 95, 110, 150, 135833, 265758, 360459, 427441, 2542860, 16883814, 137228168, 195143291, 2283242905, 19745293160, 24246846494, 92558706480 nonsquarefree numbers.

a(19) > 2*10^22. - Giovanni Resta, Nov 17 2019

Links

Table of n, a(n) for n=1..18.

Formula

Equals A000290 intersection A329472.

Example

49 is a term because sum of first five nonsquarefree numbers is a square 4 + 8 + 9 + 12 + 16 = 49.

Mathematica

p=0; Do[If[!SquareFreeQ[n], p=p+n; If[IntegerQ[p^(1/2)], Print[p]]], {n, 1, 10^8}]

Prog

(PARI) lista(nn) = {my(s=0); for(k=1, nn, if(omega(k)!=bigomega(k), s+=k; if(issquare(s), print1(s, ", ")))); } \\ Jinyuan Wang, Nov 17 2019

Crossrefs

Cf. A000290, A262783, A329472.

Sequence in context: A204233 A144656 A121275 * A188682 A354865 A191301

Adjacent sequences: A329325 A329326 A329327 * A329329 A329330 A329331

Keyword

nonn

Author

Metin Sariyar, Nov 15 2019

Extensions

a(13)-a(18) from Giovanni Resta, Nov 17 2019

Status

approved