A390289 - OEIS

%I #41 Jan 08 2026 13:20:12

%S 6,10,12,14,15,18,20,21,22,26,28,30,33,34,35,36,38,39,42,44,45,46,50,

%T 51,52,55,57,58,60,62,63,65,66,68,69,70,74,75,76,77,78,82,84,85,86,87,

%U 90,91,92,93,94,95,98,99,100,102,105,106,110,111,114,115,116,117

%N Cubefree numbers that are not prime powers.

%C Numbers with more than 1 distinct prime factor whose set of prime exponents is a subset of {1,2}.

%C Intersection of A004709 and A024619.

%C Union of A120944 and A391023, disjoint sets.

%C Union of A120944, A177492, and A386684, disjoint sets.

%C Union of A067259 \ A001248 and A120944.

%C This sequence is A377880 \ A000961.

%H Michael De Vlieger, <a href="/A390289/b390289.txt">Table of n, a(n) for n = 1..10000</a>

%e Table of n, a(n) for select n:

%e  n   a(n)

%e ---------------------

%e  1     6 = 2   *  3

%e  2    10 = 2   *  5

%e  3    12 = 2^2 *  3

%e  4    14 = 2   *  7

%e  5    15 = 3   *  5

%e  6    18 = 2   *  3^2

%e  7    20 = 2^2 *  5

%e  8    21 = 3   *  7

%e  9    22 = 2   * 11

%e 10    26 = 2   * 13

%e 16    36 = 2^2 *  3^2

%e 55   100 = 2^2 *  5^2

%t Select[Range[120], And[Length[#] > 1, SubsetQ[{1, 2}, Union[#]]] &[FactorInteger[#][[All, -1]] ] &]

%o (Python)

%o from math import isqrt

%o from sympy import mobius, integer_nthroot, primepi

%o def A390289(n):

%o     def f(x): return n+x+1-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x,3)[0]+1))+primepi(x)+primepi(isqrt(x))

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Jan 07 2026

%Y Cf. A001248, A004709, A024619, A067259, A120944, A177492, A377880, A386684, A391023.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Dec 31 2025