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

1,1

Links

Table of n, a(n) for n=1..32.

Formula

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

Example

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,

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).

Crossrefs

Cf. A025281, A001414.

Sequence in context: A306394 A109136 A295522 * A192157 A268810 A063581

Adjacent sequences: A065128 A065129 A065130 * A065132 A065133 A065134

Keyword

nonn

Author

Labos Elemer, Oct 15 2001

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

Status

approved