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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Cf. also A327859.
Sequence in context: A143113 A053544 A174879 * A094136 A051996 A242303
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)