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A328464 Square array A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1), read by descending antidiagonals.

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