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A138618
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Triangle of exponentials of Mangoldt function M(n) read by rows, in which row products give the natural numbers.
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1
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1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 5, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are A001414. This table is similar to A139547 and A120885. Cumulative column products are A003418, A139550, A139552, A139554.
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LINKS
| Weisstein, Eric W., Mangoldt Function.
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FORMULA
| T(n,k) = if n>=k then A139547((A120885-1)) else 1.
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EXAMPLE
| 1 = 1
2*1 = 2
3*1*1 = 3
2*2*1*1 = 4
5*1*1*1*1 = 5
1*3*2*1*1*1 = 6
7*1*1*1*1*1*1 = 7
2*2*1*2*1*1*1*1 = 8
3*1*3*1*1*1*1*1*1 = 9
1*5*1*1*2*1*1*1*1*1 = 10
11*1*1*1*1*1*1*1*1*1*1 = 11
1*1*2*3*1*2*1*1*1*1*1*1 = 12
13*1*1*1*1*1*1*1*1*1*1*1*1 = 13
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PROG
| (Excel cell formula) =if(mod(row(); column())=0; lookup(roundup((row()/column()); 0); A000027; A014963); 1)
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CROSSREFS
| Cf. A120885, A139547, A001414, A000027.
Sequence in context: A193870 A058564 A087157 * A140583 A123507 A188804
Adjacent sequences: A138615 A138616 A138617 * A138619 A138620 A138621
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KEYWORD
| nonn,tabl
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AUTHOR
| Mats O. Granvik (mgranvik(AT)abo.fi), May 14 2008
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