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A079474
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Triangular array: for s=0 to r-1, a(r,s) = p(s)^(r-s), where p(s) is the s-th primorial number. (p(0)=1, p(1)=2, p(2)=2*3, p(3)=2*3*5,...).
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5
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1, 1, 2, 1, 4, 6, 1, 8, 36, 30, 1, 16, 216, 900, 210, 1, 32, 1296, 27000, 44100, 2310, 1, 64, 7776, 810000, 9261000, 5336100, 30030, 1, 128, 46656, 24300000, 1944810000, 12326391000, 901800900, 510510, 1, 256, 279936, 729000000, 408410100000
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OFFSET
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1,3
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COMMENTS
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In the expansion of [1+x+x^2+...+x^(r-s)]^s, the x^n coefficient states how many factors of a(r,s) have n prime factors.
As a square array A(n,k) n>=0 k>=1 read by descending antidiagonals, A(n,k) when n>=1 is the least common period over the positive integers of the occurrence of the first n prime numbers as the k-th least operand in the respective integers' prime factorizations (written without exponents). - Peter Munn, Jan 25 2017
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LINKS
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EXAMPLE
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Triangle starts
1;
1, 2;
1, 4, 6;
1, 8, 36, 30;
1, 16, 216, 900, 210;
1, 32, 1296, 27000, 44100, 2310;
...
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MAPLE
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p:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*p(n-1)) end:
a:= (r, s)-> p(s)^(r-s):
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MATHEMATICA
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p[0] = 1; p[s_] := p[s] = Prime[s] p[s-1];
a[r_, s_] := p[s]^(r-s);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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