A065131 Arithmetic mean of first n terms of A001414 is an integer.

2, 8, 18, 26, 27, 53, 344, 539, 1221, 6869, 7271, 10753, 17742, 33289, 59688, 156649, 949350, 2291181, 3115026, 3283468, 4148225, 4493333, 18012397, 80433020, 218082214, 268274214, 639257836, 4081484513, 9373412685, 28315174578, 43438521639, 208170358834

Offset: 1

Author

Labos Elemer, Oct 15 2001

Keywords

• nonn

Examples

			Sum of first 18 terms of A001414 gives A025281(18)=126 which is divisible by n=18, so 18 is a term: 0+2+3+4+5+5+7+6+6+7+11+7+13+9+8+8+17+8=126=7*18,
		

Crossrefs

Cf. A025281, A001414.

Programs

Mathematica

s=0; Do[s=s+lg[n]; If[IntegerQ[n/25000], Print[n]]; If[IntegerQ[s/n], Print[{n, s, s/n}]], {n, 2, 2000000}] where lg[n]=A001414(n).

Formula

A025281(n)/n is an integer, where A025281(n+1)=A025281(n)+A001414(n) and A001414 is sum of primes dividing n (with repetition).

Extensions

a(21)-a(29) from Donovan Johnson, Apr 25 2010

a(30)-a(31) from Donovan Johnson, Jun 11 2011

a(32) from Donovan Johnson, Feb 26 2014