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Search: id:A103444
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| A103444 |
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Triangle read by rows: T(n,k) is number of unitary divisors of C(n,k), 0<=k<=n. |
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+0
2
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| 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 2, 4, 4, 2, 1, 1, 4, 4, 4, 4, 4, 1, 1, 2, 4, 4, 4, 4, 2, 1, 1, 2, 4, 4, 8, 4, 4, 2, 1, 1, 2, 4, 8, 8, 8, 8, 4, 2, 1, 1, 4, 4, 8, 16, 8, 16, 8, 4, 4, 1, 1, 2, 4, 8, 16, 16, 16, 16, 8, 4, 2, 1, 1, 4, 8, 8, 8, 8, 16, 8, 8, 8, 8, 4, 1, 1, 2, 8, 8, 8, 8, 16, 16, 8, 8
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OFFSET
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0,5
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COMMENT
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Row n contains n+1 terms. Row sums yield A103445.
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EXAMPLE
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T(6,3)=4 because the divisors of C(6,3)=20 are 1,2,4,5,10,20 of which 1,4,5,20 are unitary (i.e. d|20 such that gcd(d,20/d)=1).
Triangle begins:
1;
1,1;
1,2,1;
1,2,2,1;
1,2,4,2,1;
1,2,4,4,2,1;
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MAPLE
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with(numtheory):unitdiv:=proc(n) local A, k: A:={}: for k from 1 to tau(n) do if gcd(divisors(n)[k], n/divisors(n)[k])=1 then A:=A union {divisors(n)[k]} else A:=A fi od end: T:=proc(n, k) if k<=n then nops(unitdiv(binomial(n, k))) else 0 fi end: for n from 0 to 13 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A103445.
Sequence in context: A087062 A110537 A138015 this_sequence A099172 A107044 A102523
Adjacent sequences: A103441 A103442 A103443 this_sequence A103445 A103446 A103447
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 06 2005
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