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A327965
"Tamed variant" of arithmetic derivative: a(0) = a(1) = 0; for n > 1, a(n) = A327938(A003415(n)).
13
0, 0, 1, 1, 1, 1, 5, 1, 3, 6, 7, 1, 1, 1, 9, 2, 2, 1, 21, 1, 6, 10, 13, 1, 11, 10, 15, 1, 2, 1, 31, 1, 5, 14, 19, 3, 15, 1, 21, 1, 17, 1, 41, 1, 3, 39, 25, 1, 7, 14, 45, 5, 14, 1, 3, 1, 23, 22, 31, 1, 23, 1, 33, 51, 3, 18, 61, 1, 18, 26, 59, 1, 39, 1, 39, 55, 5, 18, 71, 1, 11, 1, 43, 1, 31, 22, 45, 2, 35, 1, 123, 5, 6
OFFSET
0,7
COMMENTS
Applying A327938 to the result of A003415(n) ensures that all terms stay in A048103, and that all iteration paths will (hopefully) terminate in zero. See A327966.
FORMULA
a(0) = a(1) = 0; for n > 1, a(n) = A327938(A003415(n)).
PROG
(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]%f[k, 1])); factorback(f); };
A327965(n) = if(n<=1, 0, A327938(A003415(n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved