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.

A242962 a(1) = a(2) = 0; for n >= 3: a(n) = (n*(n+1)/2) mod antisigma(n) = A000217(n) mod A024816(n).

Original entry on oeis.org

0, 0, 0, 1, 6, 3, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84
Offset: 1

Views

Author

Jaroslav Krizek, May 29 2014

Keywords

Comments

A000217(n) = triangular numbers, A024816(n) = sum of numbers less than n which do not divide n.
a(n) = sigma(n) = A000203(n) for n = 5 and n>= 7 (see A242963).

Examples

			a(6) = 3 because A000217(6) mod A024816(6) = 21 mod 9 = 3.

Links

Crossrefs

Cf. A000217, A002961, A024816, A242963, A243117, A243118.

Programs

  • Magma
    [((n*(n+1)div 2) mod (n*(n+1)div 2-SumOfDivisors(n))): n in [3..1000]]
  • Mathematica
    Array[If[# < 3, 0, Mod[PolygonalNumber@ #, Total@ Complement[Range@ #, Divisors@ #]]] &, 65] (* Michael De Vlieger, Jan 28 2020 *)

A242963 Numbers n such that A242962(n) = sigma(n) = A000203(n).

Original entry on oeis.org

5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
Offset: 1

Views

Author

Jaroslav Krizek, May 29 2014

Keywords

Comments

A242962(n) = (n*(n+1)/2) mod antisigma(n) = A000217(n) mod A024816(n).
Union of number 5 and numbers >= 7.
Conjecture: this sequence lists all the positive integers n such that, for some integer k, (sin(k*Pi/n))^2 is irrational. - Lorenzo Sauras Altuzarra, Jan 27 2020

Links

Crossrefs

Cf. A000203, A000217, A002961, A024816, A242962, A243117, A243118, A217290, A009005.

Programs

  • Magma
    [n: n in [3..100000] | ((n*(n+1)div 2) mod (n*(n+1)div 2-SumOfDivisors(n))) eq (SumOfDivisors(n))]
  • Mathematica
    Select[Range[3, 71], DivisorSigma[1, #] == Mod[PolygonalNumber@ #, Total@ Complement[Range@ #, Divisors@ #]] &] (* Michael De Vlieger, Jan 28 2020 *)

A243118 Numbers n such that A242962(x) = n has no solution.

Original entry on oeis.org

2, 4, 5, 7, 9, 10, 11, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 33, 34, 35, 37, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 58, 59, 61, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 92, 94, 95, 97, 99, 100, 101, 103, 105, 106
Offset: 1

Views

Author

Jaroslav Krizek, May 29 2014

Keywords

Comments

A242962(n) = (n*(n+1)/2) mod antisigma(n) = A000217(n) mod A024816(n); where A000217(n) = triangular numbers, A024816(n) = sum of numbers less than n which do not divide n.
Union of A007369 and numbers 4 and 7.
Complement of A243117.
a(n) = A007369(n-2) for n >= 5, where A007369 = numbers n such that sigma(x) = n has no solution.

Examples

			4 is in the sequence because there is no x whose A242962(x) = 4.

Crossrefs

Cf. A000203, A007369, A242962, A242963, A243117.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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