A384442 Smallest k such that A361373(k) = n.

1, 2, 4, 6, 10, 12, 18, 40, 36, 30, 60, 102, 84, 132, 150, 264, 210, 540, 330, 420, 660, 630, 840, 1050, 2100, 2340, 2520, 3150, 2310, 2730, 4290, 4620, 6930, 9240, 15960, 16170, 17850, 18480, 20790, 34650, 62370, 68250, 30030, 62790, 60060, 78540, 90090, 117810

Offset: 0

Author

Michael De Vlieger, Jun 12 2025

Keywords

• nonn

Comments

For n > 1, a(n) is composite, since A361373(p) = 1 for prime p.

For n = 0..2, a(n) = 2^n. For n > 2, a(n) is in A024619.

Examples

			Table of n, a(n) for n = 1..12, showing row a(n) of A377485.
          log n/log p
 n  a(n)  p_1 p_2 p_3  row n of A377485
-------------------------------------------------------------------------
 1:   2   1            {p}
 2:   4   2            {p, p^2}
 3:   6   2   1        {p, q, p^2}
 4:  10   3   1        {p, p^2, q, p^3}
 5:  12   3   2        {p, q, p^2, p^3, q^2}
 6:  18   4   2        {p, q, p^2, p^3, q^2, p^4}
 7:  40   5   2        {p, p^2, q, p^3, p^4, q^2, p^5}
 8:  36   5   3        {p, q, p^2, p^3, q^2, p^4, q^3, p^5}
 9:  30   4   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3}
10:  60   5   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3, p^5}
11: 102   6   4   1    {p, q, p^2, p^3, q^2, p^4, r, q^3, p^5, p^6, q^4}
12:  84   6   4   2    {p, q, p^2, r, p^3, q^2, p^4, q^3, p^5, r^2, p^6, q^4}
		

Crossrefs

Cf. A361373, A377845.

Programs

Mathematica

nn = 30030; t[_] := 0; u = 1; Do[(If[t[#] == 0, t[#] = n]; If[# == u, While[t[u] != 0, u++]]) &[Total@ Map[Floor@ Log[#, n] &, FactorInteger[n][[All, 1]] ] ], {n, 2, nn}]; {1}~Join~Array[t, u - 1]