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A355544
Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer.
1
1, 3, 6, 37, 75, 668, 1075, 37732, 742767, 1811865, 3140083, 8937770, 108268896, 282951249, 633932500, 1275584757, 60455590365
OFFSET
1,2
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).
EXAMPLE
3 is a term since the arithmetic mean of the first 3 squarefree numbers, (1+2+3)/3 = 2, is an integer.
MATHEMATICA
s = Select[Range[10^6], SquareFreeQ]; r = Accumulate[s]/Range[Length[s]]; ind = Position[r, _?IntegerQ] // Flatten
PROG
(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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 06 2022
EXTENSIONS
a(17) from Daniel Suteu, Jul 06 2022
STATUS
approved