cp's OEIS Frontend

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

%I A384442 #22 Jun 14 2025 00:33:41
%S A384442 1,2,4,6,10,12,18,40,36,30,60,102,84,132,150,264,210,540,330,420,660,
%T A384442 630,840,1050,2100,2340,2520,3150,2310,2730,4290,4620,6930,9240,15960,
%U A384442 16170,17850,18480,20790,34650,62370,68250,30030,62790,60060,78540,90090,117810
%N A384442 Smallest k such that A361373(k) = n.
%C A384442 For n > 1, a(n) is composite, since A361373(p) = 1 for prime p.
%C A384442 For n = 0..2, a(n) = 2^n. For n > 2, a(n) is in A024619.
%e A384442 Table of n, a(n) for n = 1..12, showing row a(n) of A377485.
%e A384442           log n/log p
%e A384442  n  a(n)  p_1 p_2 p_3  row n of A377485
%e A384442 -------------------------------------------------------------------------
%e A384442  1:   2   1            {p}
%e A384442  2:   4   2            {p, p^2}
%e A384442  3:   6   2   1        {p, q, p^2}
%e A384442  4:  10   3   1        {p, p^2, q, p^3}
%e A384442  5:  12   3   2        {p, q, p^2, p^3, q^2}
%e A384442  6:  18   4   2        {p, q, p^2, p^3, q^2, p^4}
%e A384442  7:  40   5   2        {p, p^2, q, p^3, p^4, q^2, p^5}
%e A384442  8:  36   5   3        {p, q, p^2, p^3, q^2, p^4, q^3, p^5}
%e A384442  9:  30   4   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3}
%e A384442 10:  60   5   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3, p^5}
%e A384442 11: 102   6   4   1    {p, q, p^2, p^3, q^2, p^4, r, q^3, p^5, p^6, q^4}
%e A384442 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}
%t A384442 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]
%Y A384442 Cf. A361373, A377845.
%K A384442 nonn
%O A384442 0,2
%A A384442 _Michael De Vlieger_, Jun 12 2025