A370136 Triangle read by rows: T(n,k) = arithmetic derivative of ((A002110(n) + A002110(k)) / A002110(k)), 1 <= k <= n.

1, 4, 1, 32, 5, 1, 55, 60, 12, 1, 1292, 195, 71, 16, 1, 22532, 2505, 841, 384, 9, 1, 382892, 102723, 8897, 8640, 191, 21, 1, 2469635, 3502740, 323328, 34133, 9980, 756, 24, 1, 111738812, 18755325, 10308201, 1568312, 50621, 5211, 371, 44, 1, 4853127108, 2003156919, 107924801, 178347008, 2376149, 251367, 6339, 672, 31, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..1081; the first 46 rows of triangle, flattened

Index entries for sequences related to primorial numbers

Formula

a(n) = A003415(A370135(n)).

Example

Triangle begins as:
          1;
          4,        1;
         32,        5,        1;
         55,       60,       12,       1;
       1292,      195,       71,      16,     1;
      22532,     2505,      841,     384,     9,    1;
     382892,   102723,     8897,    8640,   191,   21,   1;
    2469635,  3502740,   323328,   34133,  9980,  756,  24,  1;
  111738812, 18755325, 10308201, 1568312, 50621, 5211, 371, 44, 1;

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A370135(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2, x=A002110(1+n - binomial(c + 1, 2))); ((A002110(1+c)+x)/x); };
A370136(n) = A003415(A370135(n));

Crossrefs

Cf. A002110, A003415, A370129, A370135.

Sequence in context: A123126 A303277 A174501 * A051142 A266240 A322601

Adjacent sequences: A370133 A370134 A370135 * A370137 A370138 A370139

Keyword

nonn,tabl

Author

Antti Karttunen, Mar 07 2024

Status

approved