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%I #19 Oct 18 2019 21:29:09
%S 1,3,1,7,4,1,9,16,6,1,31,19,36,8,1,33,106,41,78,12,1,37,109,386,85,
%T 144,14,1,39,121,391,1002,155,222,18,1,211,124,421,1009,2432,235,324,
%U 20,1,213,1156,426,1079,2443,4200,341,438,24,1,217,1159,5006,1086,2575,4213,7430,457,668,30,1,219,1171,5011,17018,2586,4421,7447,12674,691,900,32,1
%N Square array A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1), read by descending antidiagonals.
%C Array is read by falling antidiagonals with n (row) and k (column) ranging as: (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
%C Row n contains all such sums of distinct primorials whose least significant summand is A002110(n-1), with each sum divided by that least significant primorial, which is also the largest primorial which divides that sum.
%H Antti Karttunen, <a href="/A328464/b328464.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1).
%F a(n) = A328461(A135764(n)). [When all sequences are considered as one-dimensional]
%e Top left 9 X 11 corner of the array:
%e 1: | 1, 3, 7, 9, 31, 33, 37, 39, 211, 213, 217
%e 2: | 1, 4, 16, 19, 106, 109, 121, 124, 1156, 1159, 1171
%e 3: | 1, 6, 36, 41, 386, 391, 421, 426, 5006, 5011, 5041
%e 4: | 1, 8, 78, 85, 1002, 1009, 1079, 1086, 17018, 17025, 17095
%e 5: | 1, 12, 144, 155, 2432, 2443, 2575, 2586, 46190, 46201, 46333
%e 6: | 1, 14, 222, 235, 4200, 4213, 4421, 4434, 96578, 96591, 96799
%e 7: | 1, 18, 324, 341, 7430, 7447, 7753, 7770, 215442, 215459, 215765
%e 8: | 1, 20, 438, 457, 12674, 12693, 13111, 13130, 392864, 392883, 393301
%e 9: | 1, 24, 668, 691, 20678, 20701, 21345, 21368, 765050, 765073, 765717
%o (PARI)
%o up_to = 105;
%o A002110(n) = prod(i=1,n,prime(i));
%o A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
%o A328464sq(n,k) = (A276156((2^(n-1)) * (k+k-1)) / A002110(n-1));
%o A328464list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A328464sq(col,(a-(col-1))))); (v); };
%o v328464 = A328464list(up_to);
%o A328464(n) = v328464[n];
%Y Cf. A328463 (transpose).
%Y Cf. A000265, A002110, A007814, A135764, A276154, A276156,
%Y Rows 1 - 5: A328462, A328465, A328466, A328467, A328468.
%Y Column 2: A008864.
%Y Column 3: A023523 (after its initial term).
%Y Column 4: A286624.
%Y Cf. also arrays A276945, A286625.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Oct 16 2019
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