A379010 - OEIS

%I #9 Dec 14 2024 11:01:08

%S 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,

%T 120,156,16,8,20,120,72,1210,192,272,18,6,54,48,420,160,2028,288,342,

%U 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

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

%C Each column is strictly increasing.

%H Antti Karttunen, <a href="/A379010/b379010.txt">Table of n, a(n) for n = 1..11325; the first 150 antidiagonals, flattened</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

%e The top left corner of the array:

%e k=  |  1     2     3      4     5      6     7        8      9     10

%e 2k= |  2     4     6      8    10     12    14       16     18     20

%e ----+-------------------------------------------------------------------

%e 1   |  1,    2,    2,     4,    4,     4,    6,       8,     6,     8,

%e 2   |  2,    6,    8,    18,   12,    24,   20,      54,    40,    36,

%e 3   |  4,   20,   24,   100,   40,   120,   48,     500,   168,   200,

%e 4   |  6,   42,   60,   294,   72,   420,   96,    2058,   660,   504,

%e 5   | 10,  110,  120,  1210,  160,  1320,  180,   13310,  1560,  1760,

%e 6   | 12,  156,  192,  2028,  216,  2496,  264,   26364,  3264,  2808,

%e 7   | 16,  272,  288,  4624,  352,  4896,  448,   78608,  5472,  5984,

%e 8   | 18,  342,  396,  6498,  504,  7524,  540,  123462,  9108,  9576,

%e 9   | 22,  506,  616, 11638,  660, 14168,  792,  267674, 17864, 15180,

%e 10  | 28,  812,  840, 23548, 1008, 24360, 1120,  682892, 26040, 29232,

%e 11  | 30,  930, 1080, 28830, 1200, 33480, 1260,  893730, 39960, 37200,

%e 12  | 36, 1332, 1440, 49284, 1512, 53280, 1656, 1823508, 59040, 55944,

%o (PARI)

%o up_to = 11325; \\ = binomial(150+1,2)

%o 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));

%o A379010sq(row,col) = eulerphi(A246278sq(row,col));

%o 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); };

%o v379010 = A379010list(up_to);

%o A379010(n) = v379010[n];

%Y Cf. A000010, A246278, A379011.

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

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Dec 14 2024