A332556 Supertotient numbers: numbers k such that the set of numbers less than k and relatively prime to k can be partitioned into two disjoint subsets of equal sum.

5, 8, 10, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87

Offset

1,1

Comments

The concept of supertotient numbers was introduced by Mahmood and Ali (2017). - Amiram Eldar, Apr 14 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Shahbaz Ali and Khalid Mahmood, New Numbers on Euler’s Totient Function with Applications, Journal of Mathematical Extension, Vol. 14, No. 1, (2020), 61-83.

Joshua Harrington, Tony W. H. Wong, On super totient numbers and super totient labelings of graphs, Discrete Mathematics Vol. 343, Iss. 2, February 2020, 111670.

M. Khalid Mahmood and Shahbaz Ali, A Novel Labeling Algorithm on Several Classes of Graphs, Punjab University Journal of Mathematics, Vol. 49, No. 2 (2017), pp. 23-35.

Formula

A023896(a(n)) == 0 (mod 2). - Amiram Eldar, Apr 14 2020

Mathematica

Select[Complement[Range[100], {1, 2, 4, 6, 18}], PrimeNu[#] > 1 || Mod[FactorInteger[#][[1, 1]], 4] != 3 &] (* Amiram Eldar, Apr 14 2020 *)

Crossrefs

Complement of A332555.

Cf. A023896.

Sequence in context: A314376 A205841 A344443 * A049195 A172019 A064362

Adjacent sequences: A332553 A332554 A332555 * A332557 A332558 A332559

Keyword

nonn

Author

N. J. A. Sloane, Feb 22 2020

Status

approved