A096366 revision #34
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A096366
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Known primitive friendly integers.
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6
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6, 12, 24, 28, 30, 40, 42, 56, 60, 80, 84, 96, 108, 135, 140, 168, 200, 210, 224, 234, 240, 264, 270, 273, 280, 360, 380, 408, 480, 496
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OFFSET
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1,1
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COMMENTS
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Friends m and n are primitive friendly iff they have no common prime factor of the same multiplicity.
There may be other primitive friendly integers within the range of those given, but they have yet to be calculated.
All perfect numbers are 2-primitive-friendly (since they are all products of distinct powers of 2 and distinct Mersenne primes). - Daniel Forgues, Jun 24 2009
A friendly integer can be both primitive and nonprimitive. For example, consider 30. First, 30 is friendly to 140, but this relation is nonprimitive, because it is 5 times the friendly pair {6, 28}. But then, 30 is also friendly to 6200, and this is a primitive pair (not a scaling of a smaller friendly pair). - Jeppe Stig Nielsen, Dec 07 2022
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LINKS
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EXAMPLE
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While 6 and 28 are not coprime because they share the common factor 2, the factor 2 appears twice in 28 but only once in 6, so they are in the sequence.
280 is primitive friendly to 1553357978368 = 2^8*7^2*19^2*37*73*127;
360 is primitive friendly to 155086041146982400 = 2^20*5^2*7^3*13*31*127*337;
380 is primitive friendly to 31701183232 = 2^8*19^2*37*73*127;
408 is primitive friendly to 874453888 = 2^7*7*11*17^2*307. (End)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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editing
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