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.

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)

Links

Table of n, a(n) for n=1..5.

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

Cf. A002110, A002620, A003415, A047257, A048103, A100716, A276085, A276086, A276156, A327859, A327860, A369650.

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

Adjacent sequences: A328107 A328108 A328109 * A328111 A328112 A328113

Keyword

nonn,hard,more

Author

Antti Karttunen, Oct 08 2019

Status

approved