cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A164280 a(n) is the sum of the first A129749(n) nonprimes.

Original entry on oeis.org

1, 64, 800, 1452, 207143, 14934568, 18656679, 42721785, 889239450, 1991045973, 6684665064, 11847007536, 127880982508860, 262907426075600, 435646635220423, 58536266213035868, 1777764795352216572, 5690843954660983949, 190101452851104748107, 71537286176000166753366
Offset: 1

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Author

Klaus Brockhaus, Aug 11 2009

Keywords

Comments

A variant of A050247 for nonprimes.

Examples

			A129749(4) = 44; sum of first 44 nonprimes is 1452, so a(4) = 1452.

Crossrefs

Cf. A129749, A050247, A018252, A160758.

Programs

  • Magma
    S:=[]; a:=0; c:=0; for n in [1..20000000] do if not IsPrime(n) then a+:=n; c+:=1; if a mod c eq 0 then Append(~S, a); end if; end if; end for; S;

Formula

a(n) = sum_{i=1..A129749(n)} A018252(i).

Extensions

a(16)-a(19) from Donovan Johnson, Sep 19 2009
a(20) from Donovan Johnson, Jun 21 2011

A179860 Integer averages of first n noncomposites for some n.

Original entry on oeis.org

1, 2, 6, 636, 1592, 2574, 292656, 917042, 1108972, 1678508, 3334890730, 3981285760, 28567166356, 32739591796, 83332116034, 871263881618, 1055495274756
Offset: 1

Views

Author

Ray Chandler, Jul 29 2010

Keywords

Comments

A variant of A050248 (primes), A073263 (composites) and A160758 (nonprimes).

Examples

			Sum of first 7 noncomposites is 42; 42 / 7 = 6 is in the sequence.

Crossrefs

Cf. A008578 (noncomposites), A014284 (sum of first n noncomposites).
Cf. A179859, A179861, A158682.

Formula

a(n) = A179861(n) / A179859(n) = A014284(A179859(n)) / A179859(n).

Extensions

a(16)-a(17) from Robert Price, Apr 21 2013

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

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Sep 09 2009

Keywords

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
Showing 1-3 of 3 results.

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