

A335081


First elements of maximal isospectral chains of length 2.


5



84, 228, 280, 340, 372, 408, 468, 480, 516, 624, 740, 792, 804, 840, 868, 880, 948, 984, 1012, 1188, 1200, 1204, 1236, 1240, 1364, 1380, 1440, 1456, 1488, 1496, 1524, 1624, 1652, 1668, 1672, 1700
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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



EXAMPLE

a(1) = 84 since both 84 an 84/2 = 42 have spectral basis {21,28,36}, while index(84) = 1 and index(42) = 2.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



