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A336568
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Numbers that are not a product of two numbers each having distinct prime multiplicities.
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23
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30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 210, 222, 230, 231, 238, 246, 255, 258, 266, 273, 282, 285, 286, 290, 310, 318, 322, 330, 345, 354, 357, 366, 370, 374, 385, 390, 399, 402, 406, 410, 418, 420, 426, 429
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OFFSET
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1,1
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COMMENTS
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First differs from A287483 in having 222.
First differs from A350352 in having 420.
A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
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LINKS
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EXAMPLE
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Selected terms together with their prime indices:
660: {1,1,2,3,5}
798: {1,2,4,8}
840: {1,1,1,2,3,4}
3120: {1,1,1,1,2,3,6}
9900: {1,1,2,2,3,3,5}
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MATHEMATICA
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strsig[n_]:=UnsameQ@@Last/@FactorInteger[n]
Select[Range[100], Function[n, Select[Divisors[n], strsig[#]&&strsig[n/#]&]=={}]]
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CROSSREFS
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A336500 has zeros at these positions.
A007425 counts divisors of divisors.
A056924 counts divisors greater than their quotient.
A074206 counts strict chains of divisors from n to 1.
A130091 lists numbers with distinct prime multiplicities.
A181796 counts divisors with distinct prime multiplicities.
A327498 is the maximum divisor with distinct prime multiplicities.
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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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