A393049 - OEIS

A393049

Composite numbers k such that k is a multiple of A276085(A003415(k)), where A003415 is the arithmetic derivative and A276085 is fully additive with a(p) = p#/p.

%I #8 Feb 10 2026 22:22:17

%S 4,6,8,9,12,15,20,21,50,64,65,95,108,135,144,160,180,189,320,329,432,

%T 481,623,869,1024,1072,1199,1280,1458,1639,2257,2700,2912,3341,3408,

%U 3456,3564,3933,4032,4511,4802,5292,6071,6750,7168,7290,7361,7500,7776,9383,11500,11664,12798,13201,13248,14580,15660,17136

%N Composite numbers k such that k is a multiple of A276085(A003415(k)), where A003415 is the arithmetic derivative and A276085 is fully additive with a(p) = p#/p.

%H Antti Karttunen, <a href="/A393049/b393049.txt">Table of n, a(n) for n = 1..1492</a>

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o is_A393049(n) = (n>1 && !isprime(n) && !(n%A276085(A003415(n))));

%Y Cf. A003415, A276085, A393050 (subsequence).

%Y Subsequence of A393048.

%Y Cf. also A373490.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 06 2026