A351038 Numbers whose maximal digit in their primorial base expansion is not larger than the maximal exponent in their prime factorization.

2, 3, 4, 6, 7, 8, 9, 12, 16, 30, 31, 32, 33, 36, 37, 38, 39, 40, 44, 45, 48, 60, 63, 64, 68, 72, 75, 76, 80, 81, 96, 104, 108, 112, 128, 144, 160, 192, 210, 211, 212, 213, 216, 217, 218, 219, 220, 224, 225, 232, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 256, 270, 272, 275, 276, 279, 280, 284, 288, 304

Offset: 1

Author

Antti Karttunen, Feb 01 2022

Keywords

• nonn
• base

Comments

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) doesn't increase.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..28472; terms <= 9699690
• Index entries for sequences related to primorial base

Crossrefs

Cf. A051903, A276086, A328114, A351039 (characteristic function), A351069 and A351070 (counts).

Positions of nonpositive terms in A350074.

Subsequences: A350075, A351075, also A369645 (after its initial 1).

Cf. also A341518.

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); };
isA351038(n) = (A051903(A276086(n)) <= A051903(n));