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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Mar 24 2021

Keywords

• nonn
• tabl

Examples

			The top left corner of the array:
   k =  1  2     3   4   5    6   7   8    9   10   11     12    13   14
  2k =  2  4     6   8  10   12  14  16   18   20   22     24    26   28
     |
-----+--------------------------------------------------------------------------
n= 1 | 1,  1,   36,  5,  2,  36, 24,  1,   9,   2,   4,    180,  18, 168,
   2 | 2,  1,  120,  4,  8,  30, 12, 11,  10,   4,   4,    240, 360,   6,
   3 | 2,  1,  336,  4, 56,  28, 12,  1, 266,  42,   4,    672, 120,   2,
   4 | 4, 19,  264,  8, 56, 418, 48,  1, 308, 798,  32,    528,  24,  38,
   5 | 2,  1, 1092,  4,  8,  26, 48,  1,  26,   6,  12,  37128,   8,  76,
   6 | 2,  1,  612, 20,  8,  34, 12,  1,  34,  12,  12,   6120,   4,   6,
   7 | 2,  1, 2280, 20, 24,  76, 20,  1,  38,   6, 152,   4560,  12,   6,
   8 | 4,  1, 5520, 40, 24, 138, 16,  1,  92,   2, 152,  11040,  24,   2,
   9 | 6,  1, 6960, 60, 12,  58, 12,  1, 174,   2,  24,  13920,  96,  14,
  10 | 2,  1, 1984,  4, 12,  62,  4,  1, 186,   2,  24, 146816, 288,   6,
  11 | 2,  3, 2812,  4,  8, 222, 32, 11,  74,  42,  12,   5624,  24,  12,
  12 | 2,  1, 3444,  4,  8,  82, 12,  1,  82,  12,  36,   6888,  12,  18,
		

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A246278, A341530.

Cf. also A341605, A341606, A341626, A341627.

Programs

PARI

up_to = 91;
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
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));
A342674sq(row,col) = A341530(A246278sq(row,col));
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); };
v342674 = A342674list(up_to);
A342674(n) = v342674[n];

Formula

A(n,k) = A341530(A246278(n,k)).