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A328110
Fixed points of A327860: numbers k for which A003415(A276086(k)) = k, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
8
0, 1, 7, 8, 2556
OFFSET
1,3
COMMENTS
Applying A276086 to these terms gives the fixed points of A327859: 1, 2, 10, 15, 5005, ..., i.e., A369650 without any of the terms of A100716.
No more terms below <= 2550136832.
From Antti Karttunen, Feb 09 2024: (Start)
The known five terms are all members of A276156, which is equal to the claim that the intersection of A048103 and A369650 is squarefree. See the example, and also comments in A351088.
Even terms here must be multiples of 4, see comment in A327860.
No terms of A047257 may occur in this sequence, which is equal to the claim that A276086(a(n)) is never a multiple of 9. See comment in A327859.
(End)
EXAMPLE
Computing A327860(2556) is easy, because it is a member of A276156, as 2556 = 6 + 30 + 210 + 2310. Therefore A327860(2556) = A003415(5*7*11*13) = (5*7*11) + (5*7*13) + (5*11*13) + (7*11*13) = 2556, and 2556 is included in this sequence. - Antti Karttunen, Feb 04 2024
PROG
(PARI)
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
isA328110(n) = (A327860(n) == n);
CROSSREFS
After two initial terms (0 & 1), a subsequence of A328118.
Subsequence of A351087 and of A351088.
Sequence in context: A156206 A226487 A360990 * A298740 A202283 A322092
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Oct 08 2019
STATUS
approved