A327862 Numbers whose arithmetic derivative is of the form 4k+2, cf. A003415.

9, 21, 25, 33, 49, 57, 65, 69, 77, 85, 93, 121, 129, 133, 135, 141, 145, 161, 169, 177, 185, 201, 205, 209, 213, 217, 221, 237, 249, 253, 265, 289, 301, 305, 309, 315, 321, 329, 341, 351, 361, 365, 375, 377, 381, 393, 413, 417, 437, 445, 453, 459, 469, 473, 481, 485, 489, 493, 495, 497, 501, 505, 517, 529, 533, 537

Offset

1,1

Comments

All terms are odd because the terms A068719 are either multiples of 4 or odd numbers.

Odd numbers k for which A064989(k) is one of the terms of A358762. - Antti Karttunen, Nov 30 2022

The second arithmetic derivative (A068346) of these numbers is odd. See A235991. - Antti Karttunen, Feb 06 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
isA327862(n) = (2==(A003415(n)%4));
k=1; n=0; while(k<105, if(isA327862(n), print1(n, ", "); k++); n++);

Crossrefs

Setwise difference A235992 \ A327864.

Setwise difference A046337 \ A360110.

Union of A369661 (k' has an even number of prime factors) and A369662 (k' has an odd number of prime factors).

Subsequences: A001248 (from its second term onward), A108181, A327978, A366890 (when sorted into ascending order), A368696, A368697.

Cf. A003415, A064989, A068346, A068719, A327863, A327865, A353495 (characteristic function).

Cf. also A235991, A358762, A358772, A358774.

Sequence in context: A188159 A272600 A359161 * A108181 A368696 A369661

Adjacent sequences: A327859 A327860 A327861 * A327863 A327864 A327865

Keyword

nonn

Author

Antti Karttunen, Sep 30 2019

Status

approved