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A341518
Numbers k such that the primorial base representation of their arithmetic derivative does not contain digits larger than 1.
6
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.
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 28 2021
STATUS
approved