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

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn

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

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.

Programs

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.