A165239 Integers of the form "partial sum of the first k nonprimes divided by the k-th nonprime.".

1, 8, 9, 46, 172, 1188, 4708, 28611, 480644, 785709, 1061769, 24947740, 31585866, 110275647, 149612794, 159273153, 396643326, 586740520, 622899752, 769642427, 979286966, 2603393493, 4102885015, 4313575355, 5075807081, 5890950206, 16152068952, 62853548947

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 09 2009

Keywords

• nonn

Comments

Integers of the form A051349(k)/A018252(k), generated by k = 1, 14, 16, 88, 334, 2345, 9328, ... - R. J. Mathar, Oct 29 2011

Examples

			(1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22)/22 = 8.
(1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22 + 24 + 25)/25 = 9.
(1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22 + 24 + 25 + 26 + 27 + 28 + 30 + 32 + 33 + 34 + 35 + 36 + 38 + 39 + 40 + 42 + 44 + 45 + 46 + 48 + 49 + 50 + 51 + 52 + 54 + 55 + 56 + 57 + 58 + 60 + 62 + 63 + 64 + 65 + 66 + 68 + 69 + 70 + 72 + 74 + 75 + 76 + 77 + 78 + 80 + 81 + 82 + 84 + 85 + 86 + 87 + 88 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 98 + 99 + 100 + 102 + 104 + 105 + 106 + 108 + 110 + 111 + 112 + 114 + 115 + 116 + 117 + 118)/118 = 46.
		

Crossrefs

Cf. A051349, A160758, A018252.

Programs

Mathematica

lst={};a=0;Do[If[ !PrimeQ[n],m=n;a+=m;If[IntegerQ[a/n]&&a!=n,AppendTo[lst,a/n]]],{n,5*9!}];lst

PARI

lista(kmax) = {my(s = 1); print1(1, ", "); forcomposite(k = 1, kmax, s += k; if(!(s%k), print1(s/k, ", ")));} \\ Amiram Eldar, May 24 2024

Extensions

a(11)-a(28) from Amiram Eldar, May 24 2024