A108161 Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.

0, 1, 3, 6, 8, 13, 19, 26, 34, 37, 47, 58, 70, 83, 97, 112, 116, 133, 151, 170, 190, 211, 233, 256, 280, 285, 311, 338, 366, 395, 425, 456, 488, 521, 555, 590, 596, 633, 671, 710, 750, 791, 833, 876, 920, 965, 1011, 1058, 1106, 1113, 1163, 1214, 1266, 1319

Offset

0,3

Links

Table of n, a(n) for n=0..53.

Example

0+1=1, 1+2=3, 3+3=6, 6+sqrt(4) = 8, ...

Mathematica

Accumulate[Table[If[IntegerQ[Sqrt[n]], Sqrt[n], n], {n, 0, 53}]] (* James C. McMahon, Feb 22 2024 *)

Prog

(PARI) lista(nn) = s=0; for(x=0, nn, if(issquare(x), s+=sqrtint(x), s+=x); print1(s, ", ")) \\ Michel Marcus, Jul 02 2017

Crossrefs

Sequence in context: A073355 A067440 A346597 * A263349 A352319 A297211

Adjacent sequences: A108158 A108159 A108160 * A108162 A108163 A108164

Keyword

easy,nonn

Author

Cino Hilliard, Jun 13 2005

Status

approved