A393048 - OEIS

A393048

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

%I #6 Feb 10 2026 10:06:12

%S 4,6,8,9,12,14,15,16,20,21,25,26,27,28,32,33,35,36,38,39,44,46,48,49,

%T 50,51,52,54,55,64,65,68,76,77,81,86,87,88,91,92,94,95,99,100,108,111,

%U 112,115,116,119,122,124,125,128,135,141,143,144,146,155,158,159,160,161,164,180,183,185,187,188,189,192,196

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

%H Antti Karttunen, <a href="/A393048/b393048.txt">Table of n, a(n) for n = 1..10000</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_A393048(n) = (n>1 && !isprime(n) && (A276085(A003415(n)) <= n));

%Y Cf. A002808, A003415, A276085, A393049 (subsequence).

%Y Cf. also A392869.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 06 2026