A359831 - OEIS

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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.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

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.

PROG

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

CROSSREFS

Setwise difference A235992 \ A359829.

Cf. A003415, A358680, A359828.

Sequence in context: A297288 A335246 A055075 * A048111 A122614 A046101

Adjacent sequences: A359828 A359829 A359830 * A359832 A359833 A359834

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 17 2023

STATUS

approved