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A356305
The least k >= 0 such that A003415(n) and A276086(n-k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
4
0, 1, 0, 0, 0, 0, 1, 0, 2, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 17, 0, 0, 0, 21, 25, 2, 0, 0, 0, 0, 0, 5, 0, 5, 6, 0, 13, 1, 0, 0, 0, 0, 2, 2, 11, 0, 20, 21, 19, 17, 24, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 4, 5, 0, 0, 2, 1, 0, 0, 0, 0, 1, 10, 12, 5, 0, 0, 0, 3, 0, 0, 0, 1, 25, 1, 84, 0, 0, 1, 2, 1, 65, 5, 0, 0, 69, 8, 96
OFFSET
0,9
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356305(n) = { my(k=0, x=A003415(n)); while(gcd(A276086(n-k), x)!=1, k++); (k); };
CROSSREFS
Cf. A003415, A276086, A356311 (positions of 0's).
Cf. also A356303, A356304.
Sequence in context: A078771 A072771 A347715 * A292247 A194016 A292256
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Nov 03 2022
STATUS
approved