A351098 Numbers k such that the maximal digit value in primorial base expansion of the arithmetic derivative of k is less than the maximal exponent in the prime factorization of k.

8, 9, 16, 24, 28, 32, 40, 45, 48, 81, 96, 108, 112, 120, 125, 128, 136, 160, 184, 189, 192, 198, 208, 212, 225, 236, 244, 250, 256, 270, 288, 296, 352, 361, 459, 507, 625, 640, 768, 800, 832, 864, 896, 928, 960, 972, 1008, 1024, 1056, 1088, 1104, 1120, 1152, 1168, 1184, 1232, 1272, 1280, 1320, 1344, 1350, 1408, 1440

Offset

1,1

Comments

Numbers k such that A328390(k) < A051903(k).

Numbers k for which A051903(A327859(n)) < A051903(k).

These seem to be rarer than A351075. All terms are nonsquarefree.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial base

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
isA351098(n) = (A328114(A003415(n)) < A051903(n));
(PARI) \\ Or see A369637.

Crossrefs

Positions of negative terms in A351097. Subsequence of A013929 and of A351099.

Cf. A003415, A051903, A276086, A327859, A328390, A369637 (characteristic function).

Cf. also A351075.

Sequence in context: A231016 A346090 A169817 * A227649 A227648 A192636

Adjacent sequences: A351095 A351096 A351097 * A351099 A351100 A351101

Keyword

nonn

Author

Antti Karttunen, Feb 03 2022

Status

approved