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 1-4 of 4 results.

A343148 Numbers k such that A083266(k) is prime.

Original entry on oeis.org

2, 6, 10, 15, 21, 26, 28, 30, 35, 38, 39, 40, 42, 44, 45, 46, 51, 55, 60, 63, 68, 69, 70, 78, 84, 93, 95, 96, 102, 105, 106, 116, 123, 124, 126, 130, 135, 136, 138, 143, 146, 150, 153, 155, 166, 174, 176, 178, 201, 203, 205, 218, 219, 221, 222, 231, 232, 234, 236, 240, 244, 245, 246, 248, 249
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Apr 06 2021

Keywords

Comments

Includes 2*p for p in A157468.

Examples

			a(3) = 10 is a term because A083266(10) = 37 is prime.

Links

Crossrefs

Cf. A083266, A157468, A343151.

Programs

  • Maple
    f:= n -> numtheory:-sigma(n) + n*numtheory:-phi(n)/2 - 1:
select(t -> isprime(f(t)), [$2..1000]);
  • Mathematica
    Select[Range[250], PrimeQ[DivisorSigma[1, #] + # EulerPhi[#]/2 - 1] &] (* Michael De Vlieger, Apr 07 2021 *)

A343151 Numbers k such that 1+A083266(k) is prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 11, 19, 23, 25, 27, 36, 43, 47, 50, 64, 71, 107, 131, 163, 167, 179, 211, 223, 225, 242, 243, 251, 271, 307, 343, 359, 419, 431, 439, 443, 467, 503, 571, 691, 751, 800, 811, 827, 839, 863, 900, 907, 947, 967, 971, 991, 1019, 1031, 1058, 1063, 1091, 1103, 1187, 1279, 1296, 1331
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Apr 07 2021

Keywords

Comments

Numbers k such that the sum of divisors of k + the sum of totatives of k is prime.

Examples

			a(4) = 7 is a term because 1+A083266(n) = 29 is prime.

Links

Crossrefs

Cf. A083266, A343148. Includes A231847.

Programs

  • Maple
    f:= n -> numtheory:-sigma(n) + n*numtheory:-phi(n)/2: f(1):= 2:
select(t -> isprime(f(t)), [$1..2000]);
  • Mathematica
    {1}~Join~Select[Range[1331], PrimeQ[DivisorSigma[1, #] + # EulerPhi[#]/2] &] (* Michael De Vlieger, Apr 07 2021 *)

A083267 Product of related numbers (counted in A073757) belonging to n; related = {divisor-set, RRS}: a(n) = A007955(n)*A001783(n).

Original entry on oeis.org

1, 2, 6, 24, 120, 180, 5040, 6720, 60480, 18900, 39916800, 665280, 6227020800, 3783780, 201801600, 2075673600, 355687428096000, 496215720, 121645100408832000, 69837768000, 20858213376000, 604969665300, 25852016738884976640000, 12336143339520, 5170403347776995328000
Offset: 1

Views

Author

Labos Elemer, May 13 2003

Keywords

Examples

			For n = 10: related terms = {1,2,5,10,3,7,9}, product = 1*2*5*10*1*3*7*9 = 18900 = a(10).

Links

Crossrefs

Cf. A073757 (count), A083266 (sum), A083268 (LCM), A083267 (product), A001783, A007955.

Programs

  • Mathematica
    a[n_] := n^(DivisorSigma[0, n]/2) * Times@@ Select[Range[n], CoprimeQ[n, #] &]; Array[a, 30] (* Amiram Eldar, Jun 20 2024 *)

Extensions

More terms from Amiram Eldar, Jun 20 2024

A083268 a(n) is the lcm of related numbers to n (counted in A073757): related = {divisor-set, RRS}.

Original entry on oeis.org

1, 2, 6, 12, 60, 30, 420, 840, 2520, 630, 27720, 4620, 360360, 90090, 120120, 720720, 12252240, 1531530, 232792560, 58198140, 77597520, 29099070, 5354228880, 892371480, 26771144400, 3346393050, 80313433200, 20078358300, 2329089562800
Offset: 1

Views

Author

Labos Elemer, May 13 2003

Keywords

Examples

			For n = 10: related terms = {1,2,5,10,3,7,9}; lcm(10,1,3,7,9) = 630 = a(10).

Links

Crossrefs

Cf. A073757 (count), A083266 (sum), A083268 (LCM), A083267 (product), A038610.

Programs

  • Mathematica
    a[n_] := LCM @@ Join[{n}, Select[Range[n], CoprimeQ[n, #] &]]; Array[a, 30] (* Amiram Eldar, Jun 20 2024 *)
  • PARI
    a(n)=my(t=lcm([1..n])/n,g); while((g=gcd(t,n))>1,t/=g); t*n \\ Charles R Greathouse IV, Nov 14 2014

Formula

a(n) = lcm(n, A038610(n)).
Showing 1-4 of 4 results.

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