A369662 Numbers k whose arithmetic derivative k' is of the form 4m+2, and k' has an odd number of prime factors.

65, 77, 135, 141, 161, 185, 201, 209, 221, 301, 305, 315, 321, 341, 351, 365, 377, 381, 413, 437, 453, 481, 485, 495, 497, 501, 537, 545, 589, 649, 681, 689, 717, 721, 729, 735, 737, 745, 749, 785, 789, 849, 855, 893, 901, 905, 917, 921, 975, 989, 999, 1035, 1037, 1073, 1081, 1101, 1121, 1133, 1141, 1157, 1165

Offset: 1

Author

Antti Karttunen, Feb 06 2024

Keywords

• nonn

Comments

Equally, numbers k whose arithmetic derivative k' is congruent to 2 modulo 4 and A276085(k') is congruent to 1 modulo 4.

A003415((1/2)*A003415(a(n))) is always even.

Links

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

Crossrefs

Setwise difference A327862 \ A369661.

Cf. A003415, A276085.

Subsequences: A369664 (terms of the form 4m+1).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA369662(n) = { my(d=A003415(n)); (2==(d%4) && (bigomega(d)%2)); };