A064611 Partial sum of usigma is divisible by n, where usigma(n) = A034448(n) and summatory-usigma(n) = A064609(n).

1, 2, 8, 11, 12, 174, 212, 524, 1567, 14096, 19795, 38466, 42114, 55575, 338809, 498001, 1175281, 2424880, 3994532, 7908519, 48453784, 696840720, 5497869355, 7479239685

Offset: 1

Author

Labos Elemer, Sep 24 2001

Keywords

• nonn
• more

Comments

Analogous sequences for various arithmetical functions are A050226, A056550, A064605-A064607, A064610, A064612, A048290, A062982, A045345.

Examples

			udivisor sums[=usigma(j) values] from 1 to 8 are added: 1+3+4+5+6+12+8+9=48; it is divisible by 8, thus 8 is here.
		

Links

• Amiram Eldar, Table of n, a(n), A064609(a(n))/a(n) for n=1..24.

Crossrefs

Cf. A034448, A064609, A050226, A056550, A064605, A064606, A064607, A064610, A064612, A048290, A062982, A045345.

Programs

Mathematica

s = Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &], {n, 10^6}]; Module[{a = First@ s, b = {First@ s}}, Do[a += s[[i]]; If[Divisible[a, i], AppendTo[b, i]], {i, 2, Length@ s}]; b] (* Michael De Vlieger, Mar 18 2017 *)

Formula

A064609(n) mod n = 0.

Extensions

a(17)-a(22) from Donovan Johnson, Jul 20 2012

a(23)-a(24) from Amiram Eldar, Mar 17 2019