%I #10 Feb 04 2024 08:58:33

%S 1,2,8,9,32,240,30272,510720,223635968,6469693440,6470203776,

%T 200560520192,200793823232,304250487160832,13082767811575808,

%U 13090182069805056,32602248665739755520,1955964710091685625856,117289009331951114780672,557940862715864858896105472,558058119122955571275235328,40729680631838190048559235072

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

%H Antti Karttunen, <a href="/A369649/b369649.txt">Table of n, a(n) for n = 1..24</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

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

%e k factorization max.exp A049345(k)

%e 1 0 1

%e 2 = 2^1, 1, 10

%e 8 = 2^3, 3, 110

%e 9 = 3^2, 2, 111

%e 32 = 2^5, 5, 1010

%e 240 = 2^4 * 3 * 5, 4, 11000

%e 30272 = 2^6 * 11 * 43, 6, 1011010

%e 510720 = 2^8 * 3 * 5 * 7 * 19, 8, 10010000

%e 223635968 = 2^9 * 577 * 757, 9, 1011111110

%e 6469693440 = 2^12 * 3 * 5 * 7^3 * 307, 12, 10000010000

%e 6470203776 = 2^7 * 3 * 1151 * 14639, 7, 10010001100

%e 200560520192 = 2^10 * 43 * 4554881, 10, 100001001010

%e 200793823232 = 2^11 * 98043859, 11, 101111000010

%e 304250487160832 = 2^14 * 113 * 164336071, 14, 10001011010010

%e 13082767811575808 = 2^15 * 167 * 2390744843, 15, 100010110101110

%e 13090182069805056 = 2^13 * 3^4 * 5939 * 3321677, 13, 101000000010100.

%e Max. exp. column, which is equal to A051903(k) is most probably a permutation of nonnegative integers.

%e Note that the last column is equal to A007088(A369648(n)).

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

%Y Cf. also A369647.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 03 2024