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

1,1

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

Prog

(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));

Crossrefs

Setwise difference A373478 \ A373475.

Subsequence of A008591.

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

Sequence in context: A335671 A337628 A129957 * A328408 A198956 A110205

Adjacent sequences: A373476 A373477 A373478 * A373480 A373481 A373482

Keyword

nonn

Author

Antti Karttunen, Jun 07 2024

Status

approved