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A335083 First elements of maximal isospectral chains of length 4. 5
488880, 1525680, 2870280, 4930272, 5890248, 6374664, 8862984, 9658080, 9739080, 10338480, 10544544, 12719880, 13985712, 14777280, 15543216, 16109280, 16293600, 16682400, 16747848, 17722080, 19376136, 20822472, 22178736, 22842288, 25517232, 26056368, 26927280 (list; graph; refs; listen; history; text; internal format)
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.
Garret Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4 (April 2001), pp. 336-346.
a(1) = 488880 since all four numbers, 488880/k, k=1..4, have spectral basis {91665, 108640, 97776, 69840, 120960}, while index(488880/k)=k, k=1..4.
Sequence in context: A216070 A163401 A022215 * A252847 A359687 A251972
Walter Kehowski, May 24 2020

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Last modified June 12 10:07 EDT 2024. Contains 373329 sequences. (Running on oeis4.)