A373479 Numbers k such that A001414(k) and A003415(k) are both multiples of 3, but A083345(k) is not, where A001414 is the sum of prime factors with repetition, A003415 is the arithmetic derivative, and A083345(n) = A003415(n)/gcd(n,A003415(n)).

9, 27, 72, 81, 126, 180, 216, 234, 243, 315, 342, 378, 396, 450, 540, 558, 576, 585, 612, 648, 666, 693, 702, 729, 774, 828, 855, 945, 990, 1008, 1026, 1044, 1071, 1098, 1125, 1134, 1188, 1206, 1287, 1314, 1350, 1395, 1422, 1440, 1449, 1476, 1530, 1620, 1665, 1674, 1692, 1728, 1746, 1755, 1764, 1827, 1836, 1854

Offset: 1

Author

Antti Karttunen, Jun 07 2024

Keywords

• nonn

Comments

All terms are multiples of 9.

Not equal to 9*A289142, nor (after the initial term 9), equal to 3*A102217, although most of the terms are.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Setwise difference A373478 \ A373475.

Subsequence of A008591.

Cf. A001414, A003415, A083345, A102217, A289142.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
isA373479(n) = (!(A001414(n)%3) && !(A003415(n)%3) && (A083345(n)%3));