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Search: id:A133951
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| A133951 |
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a(n) = the number of "non-isolated divisors" of n!. A positive divisor k of n is non-isolated if either k-1 or k+1 also divides n. |
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3
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| 0, 2, 3, 4, 6, 11, 17, 19, 23, 27, 43, 43, 64, 74, 80, 82, 124, 124, 177, 185, 195, 214, 300, 300, 300, 328, 328, 334, 454, 454, 618, 618, 635, 677, 677, 677, 872, 936, 949, 949, 1224, 1228, 1579, 1587, 1587, 1672, 2124, 2124, 2126, 2126
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = A027423(n) - A133952(n) = A132747(A000142(n)).
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EXAMPLE
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a(6)=11 because 1,2,3,4,5,6,8,9,10,15,16 are the non-isolated divisors of 720.
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MAPLE
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with(numtheory): A:=proc(n) local div, NID, i: div:=divisors(factorial(n)): NID:={}: for i to tau(factorial(n)) do if member(div[i]-1, div)=true or member(div[i]+1, div)=true then NID:= `union`(NID, {div[i]}) else end if end do: NID end proc: seq(nops(A(n)), n=1..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 12 2007
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CROSSREFS
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Cf. A133952, A027423.
Sequence in context: A079310 A116853 A066615 this_sequence A111124 A117308 A114412
Adjacent sequences: A133948 A133949 A133950 this_sequence A133952 A133953 A133954
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KEYWORD
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more,nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Sep 30 2007
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EXTENSIONS
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Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 12 2007
a(31)-a(35) from Ray Chandler (rayjchandler(AT)sbcglobal.net), May 28 2008
a(36)-a(50) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 20 2008
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