A379010 Square array A(n, k) = phi(A246278(n, k)), read by falling antidiagonals; Euler totient function applied to the prime shift array.

1, 2, 2, 2, 6, 4, 4, 8, 20, 6, 4, 18, 24, 42, 10, 4, 12, 100, 60, 110, 12, 6, 24, 40, 294, 120, 156, 16, 8, 20, 120, 72, 1210, 192, 272, 18, 6, 54, 48, 420, 160, 2028, 288, 342, 22, 8, 40, 500, 96, 1320, 216, 4624, 396, 506, 28, 10, 36, 168, 2058, 180, 2496, 352, 6498, 616, 812, 30, 8, 24, 200, 660, 13310, 264, 4896, 504, 11638, 840, 930, 36

Offset

1,2

Comments

Each column is strictly increasing.

Links

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

Index entries for sequences related to prime indices in the factorization of n.

Example

The top left corner of the array:
k=  |  1     2     3      4     5      6     7        8      9     10
2k= |  2     4     6      8    10     12    14       16     18     20
----+-------------------------------------------------------------------
1   |  1,    2,    2,     4,    4,     4,    6,       8,     6,     8,
2   |  2,    6,    8,    18,   12,    24,   20,      54,    40,    36,
3   |  4,   20,   24,   100,   40,   120,   48,     500,   168,   200,
4   |  6,   42,   60,   294,   72,   420,   96,    2058,   660,   504,
5   | 10,  110,  120,  1210,  160,  1320,  180,   13310,  1560,  1760,
6   | 12,  156,  192,  2028,  216,  2496,  264,   26364,  3264,  2808,
7   | 16,  272,  288,  4624,  352,  4896,  448,   78608,  5472,  5984,
8   | 18,  342,  396,  6498,  504,  7524,  540,  123462,  9108,  9576,
9   | 22,  506,  616, 11638,  660, 14168,  792,  267674, 17864, 15180,
10  | 28,  812,  840, 23548, 1008, 24360, 1120,  682892, 26040, 29232,
11  | 30,  930, 1080, 28830, 1200, 33480, 1260,  893730, 39960, 37200,
12  | 36, 1332, 1440, 49284, 1512, 53280, 1656, 1823508, 59040, 55944,

Prog

(PARI)
up_to = 11325; \\ = binomial(150+1, 2)
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));
A379010sq(row, col) = eulerphi(A246278sq(row, col));
A379010list(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] = A379010sq(col, (a-(col-1))))); (v); };
v379010 = A379010list(up_to);
A379010(n) = v379010[n];

Crossrefs

Cf. A000010, A246278, A379011.

Cf. A062570 (row 1), A006093 (column 1), A036689 (column 2), A083553 (column 3), A135177 (column 4).

Sequence in context: A194949 A227550 A286384 * A099259 A131904 A278264

Adjacent sequences: A379007 A379008 A379009 * A379011 A379012 A379013

Keyword

nonn,tabl,new

Author

Antti Karttunen, Dec 14 2024

Status

approved