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 A335082 First elements of maximal isospectral chains of length 3. 5
 10980, 35280, 36180, 43380, 46980, 47268, 52164, 59508, 71604, 73476, 75780, 87444, 92880, 94500, 100980, 101700, 108180, 122580, 132480, 139284, 150948, 151956, 172980, 176580, 179172, 198576, 201168, 202464, 215424, 235188, 237384, 237780, 241380, 245556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Isospectral Chain Conjecture: There exist isospectral chains of any positive length. A number N is the first element of a maximal isospectral chain of length n if it is not part of an isospectral chain of length greater than n. Two integers are isospectral if they have the same spectral basis. An isospectral chain of length n is a sequence N1,...,Nn of integers with the same spectral basis such that N1=2*N2=...=n*Nn and index(Nk)=k. A chain is maximal if it cannot be extended to an isospectral chain of length n+1. The spectral sum of an integer N with at least two prime factors is the sum of the elements of its spectral basis, and is of the form k*N+1, where k is a positive integer. Then we say that N has index k, index(N)=k. LINKS Table of n, a(n) for n=1..34. Garret Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4 (April 2001), pp. 336-346. Wikipedia, Idempotent (ring theory) Wikipedia, Peirce decomposition EXAMPLE a(1) = 10980 since the three numbers 10980, 10980/2 = 5490, and 10980/3 = 3660 all have spectral basis {2745, 2440, 2196, 3600}, while index(10980) = 1, index(5490) = 2, and index(3660) = 3. CROSSREFS Cf. A330849, A335080, A335081, A335083, A335084, A335085. Sequence in context: A124668 A270148 A270115 * A104323 A252039 A252033 Adjacent sequences: A335079 A335080 A335081 * A335083 A335084 A335085 KEYWORD nonn AUTHOR Walter Kehowski, May 24 2020 STATUS approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)