A372563 Square array A(n, k) = A246278(1+n, k) - sigma(A246278(n, k)), read by falling antidiagonals, where A246278 is the prime shift array.

0, 2, 1, 3, 12, 1, 12, 11, 18, 3, 3, 85, 29, 64, 1, 17, 23, 187, 47, 36, 3, 9, 97, 19, 931, 53, 106, 1, 50, 17, 291, 75, 733, 71, 54, 3, 36, 504, 35, 889, 31, 2533, 77, 148, 5, 21, 121, 1620, 65, 1011, 111, 1639, 187, 288, 1, 3, 171, 505, 11840, 59, 2197, 119, 4927, 179, 90, 5

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..11325; the first 150 antidiagonals, flattened

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

A(n, k) = A286385(A246278(n, k)) = A246278(1+n, k) - A355927(n, k).

Example

The top left corner of the array:
k=   1    2    3      4    5      6    7       8      9     10   11      12
2k=  2    4    6      8   10     12   14      16     18     20   22      24
---+-------------------------------------------------------------------------
1  | 0,   2,   3,    12,   3,    17,   9,     50,    36,    21,   3,     75,
2  | 1,  12,  11,    85,  23,    97,  17,    504,   121,   171,  29,    635,
3  | 1,  18,  29,   187,  19,   291,  35,   1620,   505,   265,  25,   2525,
4  | 3,  64,  47,   931,  75,   889,  65,  11840,   795,  1259,  93,  12503,
5  | 1,  36,  53,   733,  31,  1011,  59,  12456,  1561,   817,  89,  16853,
6  | 3, 106,  71,  2533, 111,  2197, 157,  52580,  1839,  2987, 107,  50507,
7  | 1,  54,  77,  1639, 119,  2163,  49,  41580,  3193,  3101, 127,  53357,
8  | 3, 148, 187,  4927, 113,  6197, 211, 142280,  8283,  4969, 183, 179083,
9  | 5, 288, 179, 11669, 305,  9481, 277, 414720,  6965, 13421, 239, 374459,
10 | 1,  90, 187,  4531, 131,  7685,  73, 190980, 12649,  6303, 137, 293947,
11 | 5, 376, 301, 19869, 247, 18395, 331, 919856, 17173, 17161, 425, 906981,
12 | 3, 274, 167, 16861, 255, 13189, 349, 899540, 10335, 17099, 367, 777083,

Prog

(PARI)
up_to = 66;
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));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A286385(n) = (A003961(n)-sigma(n));
A372563sq(row, col) = A286385(A246278sq(row, col));
A372563list(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] = A372563sq(col, (a-(col-1))))); (v); };
v372563 = A372563list(up_to);
A372563(n) = v372563[n];

Crossrefs

Cf. A000203, A003961, A246278, A286385, A355927.

Cf. A046933 (column 1).

Cf. also A355924, A372562.

Sequence in context: A122050 A081323 A173958 * A175243 A168217 A329025

Adjacent sequences: A372560 A372561 A372562 * A372564 A372565 A372566

Keyword

nonn,tabl

Author

Antti Karttunen, May 21 2024

Status

approved