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A351954
Arithmetic derivative without its inherited divisor applied to the prime shadow of the factorial base exp-function: a(n) = A342001(A181819(A276076(n))).
6
0, 1, 1, 2, 1, 5, 1, 2, 2, 3, 5, 8, 1, 5, 5, 8, 2, 7, 1, 7, 7, 12, 8, 31, 1, 2, 2, 3, 5, 8, 2, 3, 3, 4, 8, 11, 5, 8, 8, 11, 7, 10, 7, 12, 12, 17, 31, 46, 1, 5, 5, 8, 2, 7, 5, 8, 8, 11, 7, 10, 2, 7, 7, 10, 3, 9, 8, 31, 31, 46, 13, 41, 1, 7, 7, 12, 8, 31, 7, 12, 12, 17, 31, 46, 8, 31, 31, 46, 13, 41, 2, 9, 9, 14, 11
OFFSET
0,4
COMMENTS
Compare the scatter plot to those of A275735, A353575 and of A353577. - Antti Karttunen, Apr 30 2022
FORMULA
a(n) = A342001(A275735(n)) = A351945(A276076(n)).
a(n) = A353577(A351576(n)). - Antti Karttunen, Apr 30 2022
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A276076(n) = { my(i=0, m=1, f=1, nextf); while((n>0), i=i+1; nextf = (i+1)*f; if((n%nextf), m*=(prime(i)^((n%nextf)/f)); n-=(n%nextf)); f=nextf); m; };
A342001(n) = (A003415(n) / A003557(n));
CROSSREFS
KEYWORD
nonn,base,easy,look
AUTHOR
Antti Karttunen, Apr 02 2022
EXTENSIONS
Verbal description added to the definition by Antti Karttunen, Apr 30 2022
STATUS
approved