A359831 - OEIS

A359831

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

%I #7 Jan 17 2023 16:32:42

%S 16,32,36,48,60,64,72,80,81,84,96,100,108,112,120,128,132,135,140,144,

%T 156,160,168,176,180,189,192,196,200,204,208,216,220,224,225,228,240,

%U 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

%N Nonprimitive elements of A235992: numbers k such that their arithmetic derivative (A003415) is even, and also for some divisor d|k, 1<d<k, both d and k/d have even derivative.

%e 16 = 4*4 is present because both 16 and 4 have even arithmetic derivative (both are in A235992).

%e 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).

%e 189 is present as 189' = 216, and 189 = 9*21, with 9' = 6 and 21' = 10.

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

%Y Setwise difference A235992 \ A359829.

%Y Cf. A003415, A358680, A359828.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jan 17 2023