A065132 Arithmetic mean of first n terms of A008472 is an integer.

2, 13, 134, 167, 2239, 62268, 75255, 135681, 439867, 18139940, 23671044, 40892256, 312083956, 724031017, 1990127567, 2144843867, 2588619526, 7439533243, 15054156002, 54892225873, 69959798320, 79760490898, 282311798922

Offset: 1

Author

Labos Elemer, Oct 15 2001

Keywords

• nonn

Examples

			Sum of first 13 terms of A008472 gives A024924(13) = 65 which is divisible by n = 13, so 13 is here: 0+2+3+2+5+5+7+2+3+7+11+5+13 = 65 = 13*5 = A024924(13).
		

Crossrefs

Cf. A024924, A008472.

Programs

Mathematica

s=0; Do[s=s+sp[n]; If[IntegerQ[n/25000], Print[n]]; If[IntegerQ[s/n], Print[{n, s, s/n}]], {n, 2, 4000000}] where sp[n]=A008472(n).

Formula

Integers n that divide A024924(n)=A008472(1)+A008472(2)+...+A008472(n).

Also, integers n that divide A024934(n).

Prime terms are listed in A143851.

Extensions

a(10)-a(19) from Donovan Johnson, Nov 22 2009

a(20)-a(23) from Donovan Johnson, Aug 31 2010