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

Author

Antti Karttunen, Sep 30 2019

Keywords

• nonn

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

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.

Programs

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++);