A392880 a(n) is the number of iterations of map k -> A392879(k) needed to reach the fixed point A392878(n), when starting iterating from k=n.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2

Offset

1,36

Comments

The number of steps to reach a term of A048103, when starting from n, and applying succesively the function A392879, which guarantees that on every step the value of A276085 stays invariant.

Positions of the first occurrence of n, for n>=0 are: 1, 4, 36, 22500, 2647102500, ..., which seems to suggest a factorization pattern 2^2 * Product_{i>=2} prime(i)^(prime(i)-1).

Links

Antti Karttunen, Table of n, a(n) for n = 1..67500

Index entries for sequences related to primorial base.

Example

For n = 5, A392879(5) = A392878(5) = 5, therefore a(5) = 0.
For n = 27 = 3^3, A392879(27) = 5, thus a(27) = 1+a(5) = 1.
For n = 36 = 2^2 * 3^2, A392879(36) = 27, thus a(36) = 1+a(27) = 2.
For n = 823543 = 7^7, A392879(n) = 11 (which is one of the fixed points), thus a(823543) = 1.
For n = 367653125 = 5^5 * 7^6, A392879(n) = 7^7 = 823543, thus a(367653125) = 1+a(7^7) = 2.
For n = 6361161361558200394723968750000 [= A380459(5005)] = 2^4 * 3^4 * 5^9 * 7^13 * 11^10,
             A392879(n) = 3578153265876487722032232421875 = 3^6 * 5^9 * 7^13 * 11^10,
           A392879^2(n) =  122707587993020840947607421875 = 5^11 * 7^13 * 11^10,
           A392879^3(n) =        615697593513781371538715 = 5^1 * 7^15 * 11^10,
           A392879^4(n) =                 109844993185235 = 5^1 * 7^1 * 11^12,
           A392879^5(n) =                            5005 = 5 * 7 * 11 * 13,
    and as A392879(5005) = 5005, we have reached a fixed point in 5 steps, thus a(n) = 5.

Prog

(PARI)
A129252(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(p)); if(pp > n, return(1))); };
A392879(n) = { my(p=A129252(n), e); if(1==p, return(n), e = valuation(n, p); (n * p^((e%p)-e) * nextprime(1+p)^(e\p))); };
A392880(n) = { my(u, c=0); while((u=A392879(n))!=n, n = u; c++); (c); };

Crossrefs

Cf. A048103 (positions of 0's), A276085, A276086, A392878, A392879.

Sequence in context: A093956 A160383 A330023 * A328891 A101436 A366247

Adjacent sequences: A392877 A392878 A392879 * A392881 A392882 A392883

Keyword

nonn

Author

Antti Karttunen, Jan 31 2026

Status

approved