A389093 Square array, A(n, k) = sigma(A389088(n, k)), read by descending antidiagonals.

3, 7, 4, 12, 13, 6, 15, 24, 31, 8, 18, 40, 48, 57, 14, 28, 32, 156, 112, 183, 12, 24, 78, 84, 400, 168, 133, 18, 31, 56, 248, 96, 2380, 216, 307, 20, 39, 121, 72, 798, 252, 1464, 360, 381, 30, 42, 124, 781, 144, 2196, 240, 5220, 600, 871, 24, 36, 104, 342, 2801, 280, 2394, 540, 7240, 720, 553, 38, 60, 72, 434, 1464, 30941, 360, 6140, 480, 25260, 912, 1407, 32

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals of the array

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Example

The top left corner of the array:
k= |  1     2     3      4     5      6     7        8      9     10    11
---+------------------------------------------------------------------------
1  |  3,    7,   12,    15,   18,    28,   24,      31,    39,    42,   36,
2  |  4,   13,   24,    40,   32,    78,   56,     121,   124,   104,   72,
3  |  6,   31,   48,   156,   84,   248,   72,     781,   342,   434,  120,
4  |  8,   57,  112,   400,   96,   798,  144,    2801,  1464,   684,  240,
5  | 14,  183,  168,  2380,  252,  2196,  280,   30941,  1862,  3294,  336,
6  | 12,  133,  216,  1464,  240,  2394,  360,   16105,  3684,  2660,  456,
7  | 18,  307,  360,  5220,  540,  6140,  432,   88741,  6858,  9210,  576,
8  | 20,  381,  600,  7240,  480, 11430,  760,  137561, 17420,  9144,  840,
9  | 30,  871,  720, 25260, 1140, 20904,  960,  732541, 16590, 33098, 1320,
10 | 24,  553,  912, 12720,  768, 21014, 1008,  292561, 33768, 17696, 1296,
11 | 38, 1407, 1216, 52060, 1596, 45024, 1672, 1926221, 37734, 59094, 1824,

Prog

(PARI)
up_to = 22155;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
A108546list(up_to) = { my(v=vector(up_to), p, q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4, up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
v108546 = A108546list(up_to);
A108546(n) = v108546[n];
A108548(n) = { my(f=factor(n)); f[, 1] = apply(A108546, apply(primepi, f[, 1])); factorback(f); };
A332806list(up_to) = { my(v=vector(2), xs=Map(), lista=List([]), p, q, u); v[2] = 3; v[1] = 5; mapput(xs, 1, 1); mapput(xs, 2, 2); mapput(xs, 3, 3);  for(n=4, up_to, p = v[2-(n%2)]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[2-(n%2)] = q; mapput(xs, primepi(q), n)); for(i=1, oo, if(!mapisdefined(xs, i, &u), return(Vec(lista)), listput(lista, prime(u)))); };
v332806 = A332806list(up_to);
A332806(n) = v332806[n];
A332808(n) = { my(f=factor(n)); f[, 1] = apply(A332806, apply(primepi, f[, 1])); factorback(f); };
A332818(n) = A108548(A003961(A332808(n)));
A389088sq(row, col) = { my(x=2*col); for(i=2, row, x = A332818(x)); (x); };
A389093sq(row, col)  = sigma(A389088sq(row, col));
A389093list(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] = A389093sq(col, (a-(col-1))))); (v); };
v389093 = A389093list(up_to);
A389093(n) = v389093[n];

Crossrefs

Cf. A000203, A332818, A389088, A389094, A389095 (2-adic valuations).

Cf. also A355927.

Sequence in context: A352709 A216627 A355927 * A365724 A112305 A231396

Adjacent sequences: A389090 A389091 A389092 * A389094 A389095 A389096

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 24 2025

Status

approved