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A350075
Numbers whose maximal digit in their primorial base expansion is less than the maximal exponent in their prime factorization.
10
8, 9, 16, 32, 36, 40, 48, 64, 72, 80, 81, 96, 112, 128, 212, 216, 224, 240, 242, 243, 248, 250, 256, 270, 272, 280, 288, 304, 320, 352, 384, 424, 432, 448, 456, 459, 464, 480, 486, 488, 496, 512, 528, 544, 576, 640, 648, 672, 704, 720, 729, 736, 768, 864, 896, 928, 960, 972, 1024, 1088, 1152, 1216, 1280, 1408, 1536, 2048
OFFSET
1,1
COMMENTS
Numbers k for which the maximal prime exponent of A276086(k) is less than the maximal prime exponent of k, A051903(k).
Numbers k for which A328114(k) < A051903(k).
Numbers such that when the map x -> A276086(x) is applied to them, the maximal exponent in the prime factorization (A051903) decreases.
EXAMPLE
In primorial base (see A049345) 9 = 3^2 is written as "111" (because 1*6 + 1*2 + 1*1 = 9), whose maximal digit (1) is less than the maximal exponent in the prime factorization of 9 (2), therefore 9 is included in this sequence.
In primorial base 2048 = 2^11 is written as "95110", whose maximal digit 9 is less than 11, therefore 2048 is included in this sequence.
PROG
(PARI)
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA350075(n) = (A051903(A276086(n)) < A051903(n));
CROSSREFS
Cf. A049345, A051903, A276086, A328114, A350076 (complement), A351067 and A351068 (counts).
Positions of negative terms in A350074.
Subsequence of A351038.
Cf. also A351075.
Sequence in context: A145820 A227647 A175053 * A353057 A274406 A261454
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Feb 01 2022
STATUS
approved