A369639 Numbers k, not squarefree, such that the maximal digit in the primorial base representation of k' is <= 3, where k' stands for the arithmetic derivative of k, A003415.

4, 8, 9, 12, 16, 18, 24, 25, 28, 32, 36, 40, 44, 45, 48, 49, 50, 54, 56, 60, 63, 68, 76, 81, 92, 96, 98, 99, 108, 112, 120, 121, 125, 136, 147, 153, 156, 160, 175, 184, 189, 192, 196, 198, 204, 208, 212, 220, 225, 228, 234, 236, 244, 250, 252, 268, 270, 280, 284, 289, 296, 300, 315, 316, 328, 333, 338, 340, 344, 361

Offset: 1

Author

Antti Karttunen, Feb 01 2024

Keywords

• nonn

Comments

Nonsquarefree numbers k (A013929) such that A327859(k) = A276086(A003415(k)) is biquadratefree number (A046100), or equally that A328114(A003415(k)) <= 3.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A013929, A046100, A327859, A328114.

Nonsquarefree terms of A369642 form a subsequence.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
ismaxprimobasedigit_at_most(n,k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
isA369639(n) = (n>0 && !issquarefree(n) && ismaxprimobasedigit_at_most(A003415(n),3));