A369649 Numbers k in A276156 (sums of distinct primorial numbers) where the maximal exponent in the prime factorization of k attains a novel value.

1, 2, 8, 9, 32, 240, 30272, 510720, 223635968, 6469693440, 6470203776, 200560520192, 200793823232, 304250487160832, 13082767811575808, 13090182069805056, 32602248665739755520, 1955964710091685625856, 117289009331951114780672, 557940862715864858896105472, 558058119122955571275235328, 40729680631838190048559235072

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..24

Index entries for sequences related to primorial base

Formula

a(n) = A276156(A369648(n)).

Example

                  k   factorization               max.exp         A049345(k)
                  1                                  0                 1
                  2 = 2^1,                           1,               10
                  8 = 2^3,                           3,              110
                  9 = 3^2,                           2,              111
                 32 = 2^5,                           5,             1010
                240 = 2^4 * 3 * 5,                   4,            11000
              30272 = 2^6 * 11 * 43,                 6,          1011010
             510720 = 2^8 * 3 * 5 * 7 * 19,          8,         10010000
          223635968 = 2^9 * 577 * 757,               9,       1011111110
         6469693440 = 2^12 * 3 * 5 * 7^3 * 307,     12,      10000010000
         6470203776 = 2^7 * 3 * 1151 * 14639,        7,      10010001100
       200560520192 = 2^10 * 43 * 4554881,          10,     100001001010
       200793823232 = 2^11 * 98043859,              11,     101111000010
    304250487160832 = 2^14 * 113 * 164336071,       14,   10001011010010
  13082767811575808 = 2^15 * 167 * 2390744843,      15,  100010110101110
  13090182069805056 = 2^13 * 3^4 * 5939 * 3321677,  13,  101000000010100.
Max. exp. column, which is equal to A051903(k) is most probably a permutation of nonnegative integers.
Note that the last column is equal to A007088(A369648(n)).

Crossrefs

Cf. A007088, A049345, A051903, A276156, A351073, A369648.

Cf. also A369647.

Sequence in context: A088825 A337706 A368341 * A181887 A221049 A181476

Adjacent sequences: A369646 A369647 A369648 * A369650 A369651 A369652

Keyword

nonn

Author

Antti Karttunen, Feb 03 2024

Status

approved