A388285 - OEIS

%I #9 Sep 21 2025 20:40:04

%S 3,5,5,6,14,9,9,21,44,13,12,41,57,90,21,8,31,219,135,230,25,18,57,93,

%T 629,261,324,33,17,51,277,161,2529,411,560,37,15,122,111,933,345,4211,

%U 609,702,45,18,101,1094,213,2857,461,9519,831,1034,57,30,85,393,4402,387,5325,741,13337,1281,1652,61

%N Square array A(n, k) = 3*A246278(n, k) - sigma(A246278(n, k)), read by falling antidiagonals. A033885(n) = 3*n-sigma(n) as applied to the prime shift array.

%H Antti Karttunen, <a href="/A388285/b388285.txt">Table of n, a(n) for n = 1..22155; the first 210 antidiagonals</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F A(n, k) = A033885(A246278(n, k)) = 3*A246278(n, k) - A355927(n, k).

%F A(n, k) = A246278(n,k) + A378979(n, k).

%F A(n, k) = A388284(n,k) * A355925(n, k).

%e The top left corner of the array:

%e k=  |  1    2    3     4    5      6    7       8      9     10    11      12

%e 2k= |  2    4    6     8   10     12   14      16     18     20    22      24

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

%e 1   |  3,   5,   6,    9,  12,     8,  18,     17,    15,    18,   30,     12,

%e 2   |  5,  14,  21,   41,  31,    57,  51,    122,   101,    85,   61,    165,

%e 3   |  9,  44,  57,  219,  93,   277, 111,   1094,   393,   453,  147,   1377,

%e 4   | 13,  90, 135,  629, 161,   933, 213,   4402,  1477,  1113,  239,   6519,

%e 5   | 21, 230, 261, 2529, 345,  2857, 387,  27818,  3381,  3777,  471,  31413,

%e 6   | 25, 324, 411, 4211, 461,  5325, 561,  54742,  6973,  5973,  711,  69207,

%e 7   | 33, 560, 609, 9519, 741, 10333, 939, 161822, 11553, 12573, 1005, 175641,

%e Columns 60 and 90:

%e k=  |       60                90

%e 2k= |      120               180

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

%e 1   |        0,               -6,

%e 2   |      915,             1501,

%e 3   |    13899,            19221,

%e 4   |    79947,           125097,

%e 5   |   513525,           604797,

%e 6   |  1272093,          1660317,

%e 7   |  3935343,          4391493,

%e 8   |  8512059,         10293513,

%e 9   | 20603199,         25961461,

%o (PARI)

%o up_to = 66;

%o A033885(n) = (3*n-sigma(n));

%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 A388285sq(row,col) = A033885(A246278sq(row,col));

%o A388285list(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] = A388285sq(col,(a-(col-1))))); (v); };

%o v388285 = A388285list(up_to);

%o A388285(n) = v388285[n];

%Y Cf. A033885, A246278, A355925, A355927, A378979, A388284.

%K sign,tabl

%O 1,1

%A _Antti Karttunen_, Sep 21 2025