A350075 Numbers whose maximal digit in their primorial base expansion is less than the maximal exponent in their prime factorization.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..13544; terms less than 9699690

Index entries for sequences related to primorial base

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

Adjacent sequences: A350072 A350073 A350074 * A350076 A350077 A350078

Keyword

nonn,base

Author

Antti Karttunen, Feb 01 2022

Status

approved