A362287 Hypertotient numbers: numbers k such that the set that includes k and the numbers less than k and relatively prime to k can be partitioned into two disjoint subsets of equal sum.

3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 31, 32, 34, 36, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 54, 56, 58, 59, 60, 62, 64, 66, 67, 68, 70, 71, 72, 74, 76, 78, 79, 80, 81, 82, 83, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 103

Offset

1,1

Comments

With the exception of 10 and 30, these are numbers k such that k*(phi(k)+2) is divisible by 4, where phi is the Euler totient function (A000010).

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), pp. 61-83.

Example

6 is a term since the set {1, 5, 6} can be partitioned into two disjoint subsets, {1, 5} and {6}, of equal sum.

Mathematica

Select[Range[120], ! MemberQ[{10, 30}, #] && Divisible[# * (EulerPhi[#] + 2), 4] &]

Prog

(PARI) is(n) = n != 10 && n != 30 && !((n * (eulerphi(n) + 2)) % 4);

Crossrefs

Cf. A000010, A332556.

Sequence in context: A039064 A187953 A188024 * A179872 A298644 A075747

Adjacent sequences: A362284 A362285 A362286 * A362288 A362289 A362290

Keyword

nonn

Author

Amiram Eldar, Apr 14 2023

Status

approved