A359831 Nonprimitive elements of A235992: numbers k such that their arithmetic derivative (A003415) is even, and also for some divisor d|k, 1

16, 32, 36, 48, 60, 64, 72, 80, 81, 84, 96, 100, 108, 112, 120, 128, 132, 135, 140, 144, 156, 160, 168, 176, 180, 189, 192, 196, 200, 204, 208, 216, 220, 224, 225, 228, 240, 252, 256, 260, 264, 272, 276, 280, 288, 297, 300, 304, 308, 312, 315, 320, 324, 336, 340, 348, 351, 352, 360, 364, 368, 372, 375

Offset: 1

Author

Antti Karttunen, Jan 17 2023

Keywords

• nonn

Examples

			16 = 4*4 is present because both 16 and 4 have even arithmetic derivative (both are in A235992).
160 is present as 160' = A003415(160) = 336, which is an even number, and 160 = 8*20, with 8' = 12 and 20' = 24 both even. Note that there is also another pair of divisors that make 160 nonprimitive, as 160 = 12*15, and also 12' = 16 and 15' = 8 are both even. (Same is true for 4*40).
189 is present as 189' = 216, and 189 = 9*21, with 9' = 6 and 21' = 10.
		

Crossrefs

Setwise difference A235992 \ A359829.

Cf. A003415, A358680, A359828.

Programs

PARI

isA359831(n) = (A358680(n) && !A359828(n)); \\ See program in A359828.