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

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

A160758 Integer averages of first n nonprime numbers for some n.

Original entry on oeis.org

1, 8, 25, 33, 359, 2948, 3291, 4959, 22350, 33357, 60907, 80962, 8276347, 11856980, 15254419, 176009996, 967538242, 1729774831, 9977169279, 193005936726
Offset: 1

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Author

Daniel Tisdale, May 25 2009

Keywords

Comments

A variant of A050248 for nonprimes.
Numbers n such that (1/n)*sum(j=1..n, A018252(j)) is an integer. - Robert G. Wilson v, Jun 05 2009

Examples

			The sum of the first 44 nonprimes is 1452. 1452 / 44 = 33, hence 33 is in the sequence.
		

Crossrefs

Cf. A050248, integer averages of n primes for some n.

Programs

  • Magma
    S:=[]; a:=0; c:=0; for n in [1..40000000] do if not IsPrime(n) then a+:=n; c+:=1; if a mod c eq 0 then Append(~S, a div c); end if; end if; end for; S; // Klaus Brockhaus, Aug 11 2009
  • Mathematica
    lst = {}; s = 0; c = 0; k = 1; While[k < 2700000000, If[ !PrimeQ@k, c++; s = s + k; If[Mod[s, c] == 0, AppendTo[lst, s/c]]]; k++ ]; lst (* Robert G. Wilson v, Jun 05 2009 *)
    a=0;lst={};Do[If[ !PrimeQ[n],m=n;a+=m;If[a/n==IntegerPart[a/n],AppendTo[lst,a/n]]],{n,9!}];lst

Formula

a(n) = A164280(n) / A129749(n).

Extensions

a(6) - a(16) from Robert G. Wilson v, Jun 05 2009
a(17) - a(19) from Donovan Johnson, Sep 16 2009
Edited by N. J. A. Sloane, May 11 2010
a(20) from Donovan Johnson, May 20 2010

A179859 Numbers k that divide the sum of the first k noncomposites.

Original entry on oeis.org

1, 3, 7, 225, 487, 735, 50047, 142835, 170209, 249655, 316585343, 374788043, 2460457827, 2803329305, 6860334657, 65397031525, 78658228039
Offset: 1

Views

Author

Ray Chandler, Jul 29 2010

Keywords

Comments

A variant of A045345 (primes), A053781 (composites) and A129749 (nonprimes).

Examples

			The sum of the first 7 noncomposites is 42 = 6*7, so 7 is in the sequence.
		

Crossrefs

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

Programs

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

Formula

Numbers k such that k | A014284(k).
a(n) = A179861(n) / A179860(n).
a(n+1) = A158682(n) + 1.

Extensions

a(16)-a(17) from Amiram Eldar, May 24 2024
Showing 1-3 of 3 results.