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A212646
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a(n) = number of Abelian groups of order A181800(n) (n-th powerful number that is the first integer of its prime signature).
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1
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1, 2, 3, 5, 7, 4, 11, 6, 15, 10, 9, 22, 14, 15, 30, 22, 21, 8, 42, 30, 25, 33, 12, 56, 44, 35, 45, 20, 77, 60, 55, 18, 66, 28, 49, 101, 84, 75, 30, 90, 44, 77, 135, 112, 110, 42, 27, 126, 60, 105, 50, 176, 154, 150, 66, 16, 121, 45, 168, 88, 154, 70, 231, 202
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OFFSET
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1,2
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COMMENTS
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The number of Abelian groups of order n, or A000688(n), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A000688 for each second signature in order of its first appearance.
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LINKS
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FORMULA
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EXAMPLE
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There are 6 Abelian groups of order 72, corresponding to the 6 factorizations of 72 into prime powers: 2^3*3^2, 2^3*3*3, 2^2*2*3^2, 2^2*2*3*3, 2*2*2*3^2, and 2*2*2*3*3. Since 72 = A181800(8), a(8) = 6.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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