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

1,1

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

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

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.

Sequence in context: A233576 A128170 A018490 * A113498 A036796 A209643

Adjacent sequences: A351035 A351036 A351037 * A351039 A351040 A351041

Keyword

nonn,base

Author

Antti Karttunen, Feb 01 2022

Status

approved