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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 11 16:20 EDT 2024. Contains 375836 sequences. (Running on oeis4.)