A327859 a(n) = A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Index entries for sequences related to primorial base

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); };
A327859(n) = A276086(A003415(n));

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: A155936 A167594 A108462 * A343824 A182106 A308037

Adjacent sequences: A327856 A327857 A327858 * A327860 A327861 A327862

Keyword

nonn,base

Author

Antti Karttunen, Sep 30 2019

Status

approved