A392360 Nonsquarefree numbers that are neither squareful or biquadratefree.

48, 80, 96, 112, 160, 162, 176, 192, 208, 224, 240, 272, 304, 320, 336, 352, 368, 384, 405, 416, 448, 464, 480, 486, 496, 528, 544, 560, 567, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 810, 816, 832, 848, 880, 891, 896, 912, 928, 944, 960, 976

Offset

1,1

Comments

Intersection of A332785 and A391115.

Numbers k such that the smallest prime power factor exponent is 1 and the largest exceeds 3.

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    48 = 2^4 *  3
 2    80 = 2^4 *  5
 3    96 = 2^5 *  3
 4   112 = 2^4 *  7
 5   160 = 2^5 *  5
 6   162 = 2   *  3^4
 7   176 = 2^4 * 11
 8   192 = 2^6 *  3
 9   208 = 2^4 * 13
10   224 = 2^5 *  7
11   240 = 2^4 *  3 * 5
19   405 = 3^4 *  5

Mathematica

Select[Range[1000], And[Min[#] == 1, AnyTrue[#, # > 3 &]] &@ FactorInteger[#][[;; , -1]] &]

Prog

(PARI) is_A392360(n) = if(n<=1, 0, (e->(vecmin(e)==1 && vecmax(e)>3))(factor(n)[, 2])); \\ Antti Karttunen, Jan 22 2026

Crossrefs

Cf. A013929, A024619, A046101, A052485, A126706, A332785, A391115.

Sequence in context: A391115 A391591 A348527 * A362969 A110229 A108608

Adjacent sequences: A392357 A392358 A392359 * A392361 A392362 A392363

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 18 2026

Status

approved