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

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

Author

Jaroslav Krizek, May 29 2014

Keywords

• nonn

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

• Michael De Vlieger, Table of n, a(n) for n = 1..14995

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 *)