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A370129
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Triangle read by rows: T(n,k) = A003415(A002110(n)+A002110(k)), 0 <= k <= n; arithmetic derivatives of the sums of two primorial numbers.
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6
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1, 1, 4, 1, 12, 16, 1, 80, 60, 92, 1, 216, 540, 608, 704, 1, 3740, 3100, 4548, 6324, 8164, 568, 60080, 40060, 56292, 116208, 61768, 110752, 33975, 1021040, 1041768, 794468, 2415104, 1091004, 1357128, 1942844, 28300, 9789116, 29099520, 19722884, 18576860, 35347200, 35779644, 26575580, 37935056, 704080, 335024060
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OFFSET
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0,3
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COMMENTS
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Apart from those positions (A014545) at the left edge where a(n) = 1, a(n) <= A087112(1+n) only at n=2, 4 and 5, i.e., never after the third row.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins as:
1;
1, 4;
1, 12, 16;
1, 80, 60, 92;
1, 216, 540, 608, 704;
1, 3740, 3100, 4548, 6324, 8164;
568, 60080, 40060, 56292, 116208, 61768, 110752;
33975, 1021040, 1041768, 794468, 2415104, 1091004, 1357128, 1942844;
28300, 9789116, 29099520, 19722884, 18576860, 35347200, 35779644, 26575580, 37935056;
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PROG
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(PARI)
A002110(n) = prod(i=1, n, prime(i));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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CROSSREFS
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Cf. also A024451 (arithmetic derivatives of primorials).
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KEYWORD
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AUTHOR
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STATUS
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approved
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