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A337470
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Square array read by falling antidiagonals, where A(n,k) = primorial inflation of k prime shifted n times with A003961.
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5
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1, 2, 1, 6, 3, 1, 4, 15, 5, 1, 30, 9, 35, 7, 1, 12, 105, 25, 77, 11, 1, 210, 45, 385, 49, 143, 13, 1, 8, 1155, 175, 1001, 121, 221, 17, 1, 36, 27, 5005, 539, 2431, 169, 323, 19, 1, 60, 225, 125, 17017, 1573, 4199, 289, 437, 23, 1, 2310, 315, 1225, 343, 46189, 2873, 7429, 361, 667, 29, 1, 24, 15015, 1925, 5929, 1331, 96577, 5491, 12673, 529, 899, 31
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OFFSET
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0,2
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COMMENTS
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Array is read by descending antidiagonals with n >= 0 and k >= 1 ranging as: (0, 1), (0, 2), (1, 1), (0, 3), (1, 2), (2, 1), (0, 4), (1, 3), (2, 2), (3, 1), ...
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LINKS
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FORMULA
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EXAMPLE
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The top left corner of the array begins as:
n/k | 1 2 3 4 5 6 7 8 9 10
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0 | 1, 2, 6, 4, 30, 12, 210, 8, 36, 60, ...
1 | 1, 3, 15, 9, 105, 45, 1155, 27, 225, 315, ...
2 | 1, 5, 35, 25, 385, 175, 5005, 125, 1225, 1925, ...
3 | 1, 7, 77, 49, 1001, 539, 17017, 343, 5929, 7007, ...
4 | 1, 11, 143, 121, 2431, 1573, 46189, 1331, 20449, 26741, ...
5 | 1, 13, 221, 169, 4199, 2873, 96577, 2197, 48841, 54587, ...
etc.
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PROG
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(PARI)
up_to = 105-1; \\ Or 78-1.
Ashifted_primorial(n, d) = prod(i=1, primepi(n), prime(i+d));
A337470sq(n, k) = { my(f=factor(k)); prod(i=1, #f~, Ashifted_primorial(f[i, 1], n)^f[i, 2]); };
A337470list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(b=1, a, i++; if(i > #v, return(v)); v[i] = A337470sq(b-1, (a-(b-1))))); (v); };
v337470 = A337470list(up_to);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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