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

1,3

Links

Table of n, a(n) for n=1..91.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

Example

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,

Prog

(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];

Crossrefs

Cf. A000203, A003961, A246278, A341530.

Cf. also A341605, A341606, A341626, A341627.

Sequence in context: A133013 A032369 A134729 * A309209 A094716 A094725

Adjacent sequences: A342671 A342672 A342673 * A342675 A342676 A342677

Keyword

nonn,tabl

Author

Antti Karttunen, Mar 24 2021

Status

approved