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A342674 Square array A(n,k) = A341530(A246278(n,k)), read by falling antidiagonals; A341530 as applied onto prime shift array A246278.

%I A342674 #8 Mar 28 2021 15:53:42
%S A342674 1,1,2,36,1,2,5,120,1,4,2,4,336,19,2,36,8,4,264,1,2,24,30,56,8,1092,1,
%T A342674 2,1,12,28,56,4,612,1,4,9,11,12,418,8,20,2280,1,6,2,10,1,48,26,8,20,
%U A342674 5520,1,2,4,4,266,1,48,34,24,40,6960,1,2,180,4,42,308,1,12,76,24,60,1984,3,2,18,240,4,798,26,1,20,138,12,4,2812,1,2
%N A342674 Square array A(n,k) = A341530(A246278(n,k)), read by falling antidiagonals; A341530 as applied onto prime shift array A246278.
%H A342674 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A342674 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A342674 A(n,k) = A341530(A246278(n,k)).
%e A342674 The top left corner of the array:
%e A342674    k =  1  2     3   4   5    6   7   8    9   10   11     12    13   14
%e A342674   2k =  2  4     6   8  10   12  14  16   18   20   22     24    26   28
%e A342674      |
%e A342674 -----+--------------------------------------------------------------------------
%e A342674 n= 1 | 1,  1,   36,  5,  2,  36, 24,  1,   9,   2,   4,    180,  18, 168,
%e A342674    2 | 2,  1,  120,  4,  8,  30, 12, 11,  10,   4,   4,    240, 360,   6,
%e A342674    3 | 2,  1,  336,  4, 56,  28, 12,  1, 266,  42,   4,    672, 120,   2,
%e A342674    4 | 4, 19,  264,  8, 56, 418, 48,  1, 308, 798,  32,    528,  24,  38,
%e A342674    5 | 2,  1, 1092,  4,  8,  26, 48,  1,  26,   6,  12,  37128,   8,  76,
%e A342674    6 | 2,  1,  612, 20,  8,  34, 12,  1,  34,  12,  12,   6120,   4,   6,
%e A342674    7 | 2,  1, 2280, 20, 24,  76, 20,  1,  38,   6, 152,   4560,  12,   6,
%e A342674    8 | 4,  1, 5520, 40, 24, 138, 16,  1,  92,   2, 152,  11040,  24,   2,
%e A342674    9 | 6,  1, 6960, 60, 12,  58, 12,  1, 174,   2,  24,  13920,  96,  14,
%e A342674   10 | 2,  1, 1984,  4, 12,  62,  4,  1, 186,   2,  24, 146816, 288,   6,
%e A342674   11 | 2,  3, 2812,  4,  8, 222, 32, 11,  74,  42,  12,   5624,  24,  12,
%e A342674   12 | 2,  1, 3444,  4,  8,  82, 12,  1,  82,  12,  36,   6888,  12,  18,
%o A342674 (PARI)
%o A342674 up_to = 91;
%o A342674 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A342674 A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
%o A342674 A246278sq(row,col) = if(1==row,2*col, my(f = factor(2*col)); for(i=1, #f~, f[i,1] = prime(primepi(f[i,1])+(row-1))); factorback(f));
%o A342674 A342674sq(row,col) = A341530(A246278sq(row,col));
%o A342674 A342674list(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] = A342674sq(col,(a-(col-1))))); (v); };
%o A342674 v342674 = A342674list(up_to);
%o A342674 A342674(n) = v342674[n];
%Y A342674 Cf. A000203, A003961, A246278, A341530.
%Y A342674 Cf. also A341605, A341606, A341626, A341627.
%K A342674 nonn,tabl
%O A342674 1,3
%A A342674 _Antti Karttunen_, Mar 24 2021