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A327859
a(n) = A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
34
1, 1, 2, 2, 9, 2, 18, 2, 25, 5, 10, 2, 225, 2, 30, 15, 21, 2, 750, 2, 625, 45, 50, 2, 525, 45, 150, 3750, 21, 2, 14, 2, 18375, 75, 250, 25, 49, 2, 750, 225, 735, 2, 630, 2, 875, 210, 1250, 2, 385875, 75, 1050, 375, 13125, 2, 36750, 225, 1029, 1125, 14, 2, 1029, 2, 42, 5250, 2941225, 125, 98, 2, 1225, 1875, 78750
OFFSET
0,3
COMMENTS
Sequence contains only terms of A048103.
Are there fixed points other than 1, 2, 10, 15, 5005? (There are none in the range 5006 .. 402653184.) See A369650.
Records occur at n = 0, 2, 4, 6, 8, 12, 18, 27, 32, 48, 64, 80, 144, 224, 256, 336, 448, 480, 512, 1728, ... (see also A131117).
a(n) and n are never multiples of 9 at the same time, thus the fixed points certainly exclude any terms of A008591. For a proof, consider my comment in A047257 and that A003415(9*n) is always a multiple of 3. - Antti Karttunen, Feb 08 2024
FORMULA
a(n) = A276086(A003415(n)).
a(p) = 2 for all primes p.
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); };
CROSSREFS
Cf. A003415, A008591, A048103, A131117, A276086, A327858, A327860, A341517 [= mu(a(n))], A341518 (k where a(k) is squarefree), A369641 (composite k where a(k) is squarefree), A369642.
Cf. A370114 (where a(k) is a multiple of k), A370115 (where k is a multiple of a(k)), A369650.
Sequence in context: A377296 A167594 A108462 * A343824 A182106 A308037
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Sep 30 2019
STATUS
approved