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A337205
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Square array A(n,k) read by falling antidiagonals, where row n gives the sum of the divisors of the {primorial inflation of k, from which all primes <= A000040(n) have been discarded}.
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6
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1, 3, 1, 12, 1, 1, 7, 4, 1, 1, 72, 1, 1, 1, 1, 28, 24, 1, 1, 1, 1, 576, 4, 6, 1, 1, 1, 1, 15, 192, 1, 1, 1, 1, 1, 1, 91, 1, 48, 1, 1, 1, 1, 1, 1, 168, 13, 1, 8, 1, 1, 1, 1, 1, 1, 6912, 24, 1, 1, 1, 1, 1, 1, 1, 1, 1, 60, 2304, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 96768, 4, 576, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1344, 32256, 1, 96, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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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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A(n,k) is the sum of divisors of A108951(k) from which all primes less than A000040(n) have been removed first.
A(n,k) is a multiple of A(n+1,k).
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EXAMPLE
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The top left 15 x 5 corner of the array:
----+------------------------------------------------------------------------
0 | 1, 3, 12, 7, 72, 28, 576, 15, 91, 168, 6912, 60, 96768, 1344, 546, ...
1 | 1, 1, 4, 1, 24, 4, 192, 1, 13, 24, 2304, 4, 32256, 192, 78, ...
2 | 1, 1, 1, 1, 6, 1, 48, 1, 1, 6, 576, 1, 8064, 48, 6, ...
3 | 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 96, 1, 1344, 8, 1, ...
4 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 168, 1, 1, ...
etc.
For example, the row 1 is the sum of the {primorial inflation of k, from which all primes <= prime(1) = 2 have been discarded}, that is, it is the sum of the odd divisors of the primorial inflation of k.
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PROG
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(PARI)
up_to = 105-1;
A337205sq(n, k) = if(1==k, k, my(f=factor(k), h = #f~, prevpid=primepi(f[h, 1]), e=f[h, 2], p, s=1); forstep(k=h-1, 0, -1, if(!k, pid=0, pid=primepi(f[k, 1])); forstep(j=prevpid, (1+pid), -1, if(j<=n, return(s)); p=prime(j); s *= ((p^(1+e)-1)/(p-1))); if(pid<=n, return(s)); prevpid = pid; e += f[k, 2]); (s));
A337205list(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] = A337205sq(b-1, (a-(b-1))))); (v); };
v337205 = A337205list(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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