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

Author

Antti Karttunen, Feb 01 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13544; terms less than 9699690
• Index entries for sequences related to primorial base

Crossrefs

Cf. A049345, A051903, A276086, A328114, A350076 (complement), A351067 and A351068 (counts).

Positions of negative terms in A350074.

Subsequence of A351038.

Cf. also A351075.

Programs

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));