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

1,3

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

Formula

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

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

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.

Sequence in context: A175415 A304721 A063464 * A325600 A195921 A175089

Adjacent sequences: A341515 A341516 A341517 * A341519 A341520 A341521

Keyword

nonn

Author

Antti Karttunen, Feb 28 2021

Status

approved