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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
Garret Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4 (April 2001), pp. 336-346.
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
Sequence in context: A124668 A270148 A270115 * A104323 A252039 A252033
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.)