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Search: id:A127478
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| 1, 2, 1, 3, 0, 2, 4, 2, 0, 2, 5, 0, 0, 0, 4, 6, 3, 4, 0, 0, 2, 7, 0, 0, 0, 0, 0, 6, 8, 4, 0, 4, 0, 0, 0, 4, 9, 0, 6, 0, 0, 0, 0, 0, 6, 10, 5, 0, 0, 8, 0, 0, 0, 0, 4, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 12, 6, 8, 6, 0, 4, 0, 0, 0, 0, 0, 4, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 14, 7, 0, 0, 0, 0, 12, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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If the two matrices A054523 and A054522 are commuted, the matrix product becomes A127477.
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FORMULA
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T(n,k) = sum_{j=k..n} A054523(n,j) * A054522(j,k).
T(n,n) = A000010(n) (diagonal).
sum_{k=1..n} T(n,k) = A018804(n) (row sums).
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EXAMPLE
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First few rows of the triangle are:
.1;
.2, 1;
.3, 0, 2;
.4, 2, 0, 2;
.5, 0, 0, 0, 4;
.6, 3, 4, 0, 0, 2;
.7, 0, 0, 0, 0, 0, 6;
.8, 4, 0, 4, 0, 0, 0, 4;
....
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MAPLE
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A054522 := proc(n, k) if k = 1 then 1; elif n mod k = 0 then numtheory[phi](k) ; else 0 ; fi; end:
A054523 := proc(n, k) if k = n then 1; elif n mod k = 0 then numtheory[phi](n/k) ; else 0 ; fi; end:
A127478 := proc(n, k) add( A054523(n, j)*A054522(j, k) , j=k..n) ; end: seq(seq( A127478(n, k), k=1..n), n=1..15) ;
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CROSSREFS
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Cf. A054522, A054523, A018804, A000010.
Sequence in context: A025649 A025642 A025643 this_sequence A127472 A004563 A146094
Adjacent sequences: A127475 A127476 A127477 this_sequence A127479 A127480 A127481
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 15 2007
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EXTENSIONS
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Converted comments to formulas, extended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2009
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