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

%I A369649 #10 Feb 04 2024 08:58:33
%S A369649 1,2,8,9,32,240,30272,510720,223635968,6469693440,6470203776,
%T A369649 200560520192,200793823232,304250487160832,13082767811575808,
%U A369649 13090182069805056,32602248665739755520,1955964710091685625856,117289009331951114780672,557940862715864858896105472,558058119122955571275235328,40729680631838190048559235072
%N A369649 Numbers k in A276156 (sums of distinct primorial numbers) where the maximal exponent in the prime factorization of k attains a novel value.
%H A369649 Antti Karttunen, <a href="/A369649/b369649.txt">Table of n, a(n) for n = 1..24</a>
%H A369649 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A369649 a(n) = A276156(A369648(n)).
%e A369649                   k   factorization               max.exp         A049345(k)
%e A369649                   1                                  0                 1
%e A369649                   2 = 2^1,                           1,               10
%e A369649                   8 = 2^3,                           3,              110
%e A369649                   9 = 3^2,                           2,              111
%e A369649                  32 = 2^5,                           5,             1010
%e A369649                 240 = 2^4 * 3 * 5,                   4,            11000
%e A369649               30272 = 2^6 * 11 * 43,                 6,          1011010
%e A369649              510720 = 2^8 * 3 * 5 * 7 * 19,          8,         10010000
%e A369649           223635968 = 2^9 * 577 * 757,               9,       1011111110
%e A369649          6469693440 = 2^12 * 3 * 5 * 7^3 * 307,     12,      10000010000
%e A369649          6470203776 = 2^7 * 3 * 1151 * 14639,        7,      10010001100
%e A369649        200560520192 = 2^10 * 43 * 4554881,          10,     100001001010
%e A369649        200793823232 = 2^11 * 98043859,              11,     101111000010
%e A369649     304250487160832 = 2^14 * 113 * 164336071,       14,   10001011010010
%e A369649   13082767811575808 = 2^15 * 167 * 2390744843,      15,  100010110101110
%e A369649   13090182069805056 = 2^13 * 3^4 * 5939 * 3321677,  13,  101000000010100.
%e A369649 Max. exp. column, which is equal to A051903(k) is most probably a permutation of nonnegative integers.
%e A369649 Note that the last column is equal to A007088(A369648(n)).
%Y A369649 Cf. A007088, A049345, A051903, A276156, A351073, A369648.
%Y A369649 Cf. also A369647.
%K A369649 nonn
%O A369649 1,2
%A A369649 _Antti Karttunen_, Feb 03 2024