A379499 - OEIS

%I #8 Jan 03 2025 09:32:22

%S 6,28,12,72,117,30,120,360,775,56,180,1080,1680,2793,132,336,672,

%T 19500,7392,16093,182,336,3510,3960,137200,24024,30927,306,496,1584,

%U 43400,10192,1948584,55692,88723,380,702,9801,5460,368676,40392,5228860,116280,137541,552,840,9300,488125,17136,2928926,69160,25645860,209760,292537,870

%N Square array A(n, k) = A064987(A246278(n, k)), read by falling antidiagonals; A064987(n) = n*sigma(n), applied to the prime shift array.

%C Each column is strictly monotonic.

%H Antti Karttunen, <a href="/A379499/b379499.txt">Table of n, a(n) for n = 1..11325; the first 150 antidiagonals of array</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) = A246278(n, k) * A355927(n, k).

%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 |   6,    28,    72,     120,   180,     336,   336,       496,     702,     840,

%e 2 |  12,   117,   360,    1080,   672,    3510,  1584,      9801,    9300,    6552,

%e 3 |  30,   775,  1680,   19500,  3960,   43400,  5460,    488125,   83790,  102300,

%e 4 |  56,  2793,  7392,  137200, 10192,  368676, 17136,   6725201,  901208,  508326,

%e 5 | 132, 16093, 24024, 1948584, 40392, 2928926, 50160, 235793305, 4082364, 4924458,

%o (PARI)

%o up_to = 55;

%o A064987(n) = (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 A379499sq(row,col) = A064987(A246278sq(row,col));

%o A379499list(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] = A379499sq(col,(a-(col-1))))); (v); };

%o v379499 = A379499list(up_to);

%o A379499(n) = v379499[n];

%Y Elementwise product of arrays A246278 and A355927.

%Y Cf. A000203, A003961, A064987, A379500.

%K nonn,tabl,new

%O 1,1

%A _Antti Karttunen_, Jan 02 2025