A392537 Biquadratefree numbers that are neither squareful nor squarefree.

12, 18, 20, 24, 28, 40, 44, 45, 50, 52, 54, 56, 60, 63, 68, 75, 76, 84, 88, 90, 92, 98, 99, 104, 116, 117, 120, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 164, 168, 171, 172, 175, 180, 184, 188, 189, 198, 204, 207, 212, 220, 228, 232, 234, 236

Offset

1,1

Comments

Intersection of A013929, A046100, and A052485; i.e., intersection of A046100 and A332785.

Numbers that have at least one prime factor exponent m = 1 and at least one m such that 1 < m < 4.

Numbers for which the minimum exponent in their prime factorization is 1 and the maximum exponent is either 2 or 3. - Antti Karttunen, Jan 22 2026

Using the factorization of numbers k into powers of (nonunit) squarefree numbers with distinct exponents that are powers of 2 (cf. row k of A352780), these are the numbers that factorize as i^1 * j^2 with j not divisible by i. - Peter Munn, Feb 25 2026

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

Table of n, a(n) for select n:
 n  a(n)
------------------------
 1   12 = 2^2 *  3
 2   18 = 2   *  3^2
 3   20 = 2^2 *  5
 4   24 = 2^3 *  3
 5   28 = 2^2 *  7
 6   40 = 2^3 *  5
 7   44 = 2^2 * 11
 8   45 = 3^2 *  5
 9   50 = 2   *  5^2
10   52 = 2^2 * 13
13   60 = 2^2 *  3   * 5
20   90 = 2   *  3^2 * 5

Mathematica

Select[Range[240], And[#1 == 1, 1 < #2 < 4] & @@ MinMax@ FactorInteger[#][[;; , -1]] &]

Prog

(PARI) is_A392537(n) = if(n<=1, 0, (e->(vecmin(e)==1 && bitor(vecmax(e), 1)==3))(factor(n)[, 2])); \\ Antti Karttunen, Jan 22 2026

Crossrefs

Cf. A013929, A024619, A046100, A052485, A126706, A332785, A352780.

Sequence in context: A394860 A345381 A328930 * A389227 A364996 A391026

Adjacent sequences: A392534 A392535 A392536 * A392538 A392539 A392540

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 16 2026

Status

approved