A341518 Numbers k such that the primorial base representation of their arithmetic derivative does not contain digits larger than 1.

0, 1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 23, 28, 29, 30, 31, 37, 41, 43, 45, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 79, 83, 87, 89, 97, 101, 103, 107, 108, 109, 112, 113, 127, 131, 136, 137, 139, 149, 151, 155, 157, 161, 163, 167, 173, 179, 181, 189, 191, 193, 197, 198, 199, 203, 209, 210, 211, 212, 217

Offset: 1

Author

Antti Karttunen, Feb 28 2021

Keywords

• nonn

Comments

Numbers k for which A328390(k) <= 1, numbers k such that A003415(k) is in A276156.

Numbers k such that A327859(k) = A276086(A003415(k)) is squarefree.

Links

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

Crossrefs

Cf. A003415, A005117, A049345, A276086, A276156, A327859, A328114, A328390.

Positions of nonzero terms in A341517.

Subsequences: A000040, A327978, A328232, A369647 (terms k where A051903(k) obtains novel values).

Cf. also A327969.

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); };
isA341518(n) = ismaxprimobasedigit_at_most(A003415(n),1); \\ Antti Karttunen, Feb 03 2024

Formula

For all n > 2, A328390(a(n)) = A328114(A003415(a(n))) = 1.