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

1,1

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

Prog

(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));

Crossrefs

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

Nonsquarefree terms of A369642 form a subsequence.

Sequence in context: A359869 A034030 A057109 * A069189 A371601 A283050

Adjacent sequences: A369636 A369637 A369638 * A369640 A369641 A369642

Keyword

nonn

Author

Antti Karttunen, Feb 01 2024

Status

approved