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

Author

Metin Sariyar, Nov 15 2019

Keywords

• nonn

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

Examples

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

Crossrefs

Cf. A000290, A262783, A329472.

Programs

Mathematica

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

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

Formula

Equals A000290 intersection A329472.

Extensions

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