A329728 Partial sums of A092261.

1, 4, 8, 9, 15, 27, 35, 36, 37, 55, 67, 71, 85, 109, 133, 134, 152, 155, 175, 181, 213, 249, 273, 277, 278, 320, 321, 329, 359, 431, 463, 464, 512, 566, 614, 615, 653, 713, 769, 775, 817, 913, 957, 969, 975, 1047, 1095, 1099, 1100, 1103, 1175, 1189, 1243

Offset: 1

Author

Amiram Eldar, Nov 19 2019

Keywords

• nonn

References

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 50.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80.
• Steven R. Finch, Unitarism and Infinitarism, February 25, 2004. [Cached copy, with permission of the author]
• Vaclav Kotesovec, Plot of a(n)/n^2 for n = 1..1000000

Crossrefs

Cf. A065465, A092261.

Programs

Mathematica

Accumulate[Table[Plus @@ Select[Divisors@ n, Max @@ Last /@ FactorInteger@ # == 1 && GCD[#, n/#] == 1 &], {n, 1, 53}]] (* after Michael De Vlieger at A092261 *)

Formula

Lim_{n->oo} a(n)/n^2 = 1/2 * Product_{p prime}(1 - 1/(p^2*(p+1))) = 1/2 * A065465.