A355544 Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer.

1, 3, 6, 37, 75, 668, 1075, 37732, 742767, 1811865, 3140083, 8937770, 108268896, 282951249, 633932500, 1275584757, 60455590365

Offset: 1

Author

Amiram Eldar, Jul 06 2022

Keywords

• nonn
• more

Comments

Numbers k such that A173143(k) is divisible by k.

The corresponding quotients A173143(k)/k are 1, 2, 4, 29, ..., and the corresponding values of A005117(k) are 1, 3, 7, 59, ... (see the link for more values).

Examples

			3 is a term since the arithmetic mean of the first 3 squarefree numbers, (1+2+3)/3 = 2, is an integer.
		

Links

• Amiram Eldar, Table of n, a(n), A173143(a(n))/a(n), A005117(a(n)) for n = 1..16.

Crossrefs

Cf. A005117, A173143.

Similar sequences: A045345, A050226, A056550, A064605, A064606, A064607, A064610, A064611, A064612, A048290.

Programs

Mathematica

s = Select[Range[10^6], SquareFreeQ]; r = Accumulate[s]/Range[Length[s]]; ind = Position[r, _?IntegerQ] // Flatten

PARI

upto(n) = my(s=0,k=0); forsquarefree(m=1, n, s+=m[1]; k+=1; if(s%k == 0, print1(k, ", "))); \\ Daniel Suteu, Jul 06 2022

Extensions

a(17) from Daniel Suteu, Jul 06 2022