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A337472
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Square array read by falling antidiagonals, where A(n,k) = sigma(A337470(n, k)).
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5
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1, 3, 1, 12, 4, 1, 7, 24, 6, 1, 72, 13, 48, 8, 1, 28, 192, 31, 96, 12, 1, 576, 78, 576, 57, 168, 14, 1, 15, 2304, 248, 1344, 133, 252, 18, 1, 91, 40, 8064, 684, 3024, 183, 360, 20, 1, 168, 403, 156, 24192, 1862, 5040, 307, 480, 24, 1, 6912, 624, 1767, 400, 60480, 3294, 8640, 381, 720, 30, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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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, 3, 12, 7, 72, 28, 576, 15, 91, 168, ...
1 | 1, 4, 24, 13, 192, 78, 2304, 40, 403, 624, ...
2 | 1, 6, 48, 31, 576, 248, 8064, 156, 1767, 2976, ...
3 | 1, 8, 96, 57, 1344, 684, 24192, 400, 7581, 9576, ...
4 | 1, 12, 168, 133, 3024, 1862, 60480, 1464, 24339, 33516, ...
5 | 1, 14, 252, 183, 5040, 3294, 120960, 2380, 56181, 65880, ...
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]); };
A337472sq(n, k) = sigma(A337470sq(n, k));
A337472list(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] = A337472sq(b-1, (a-(b-1))))); (v); };
v337472 = A337472list(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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