A161203 n-th square plus n-th squarefree number.

2, 6, 12, 21, 31, 43, 59, 75, 94, 114, 136, 161, 188, 217, 247, 279, 315, 353, 391, 431, 474, 518, 564, 613, 663, 715, 770, 826, 884, 946, 1008, 1075, 1142, 1211, 1282, 1354, 1428, 1505, 1583

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = n^2 + A005117(n) = A000290(n) + A005117(n).

Example

a(1) = 1^2 + 1.
a(2) = 2^2 + 2.
a(3) = 3^2 + 3.
a(4) = 4^2 + 5.

Mathematica

Module[{nn=40, sqs, sfree}, sqs=Range[nn]^2; sfree=Take[Select[Range[3nn], SquareFreeQ], nn]; Total/@Thread[{sqs, sfree}]] (* Harvey P. Dale, May 06 2012 *)

Prog

(Python)
from math import isqrt
from sympy import mobius
def A161203(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m+n**2 # Chai Wah Wu, Aug 12 2024

Crossrefs

Cf. A000290, A005117.

Sequence in context: A354895 A214916 A323291 * A292768 A352990 A184637

Adjacent sequences: A161200 A161201 A161202 * A161204 A161205 A161206

Keyword

nonn,easy,changed

Author

Jonathan Vos Post, Jan 20 2011

Extensions

Corrected (75 inserted) by Harvey P. Dale, May 06 2012

Status

approved