A369958 - OEIS

%I #10 Feb 07 2024 20:27:46

%S 6,30,33,42,63,210,212,213,214,220,420,429,462,2310,2312,2313,2314,

%T 2315,2316,2317,2318,2319,2320,2325,2330,2340,2342,2343,2344,2345,

%U 2346,2355,2370,2373,2379,2380,2520,2522,2526,2530,2535,2552,2730,3003,4620,4622,4623,4626,4628,4630,4654,4680,4830,4836,4862,6930,6942,7150

%N Numbers k such that A003415(k)/gcd(k, A003415(k)) >= A276086(k)/gcd(k, A276086(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A369958/b369958.txt">Table of n, a(n) for n = 1..13305  (terms up to 3*A002110(9))</a>

%F {k | A083345(k) >= A351251(k)}.

%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 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o isA369958(n) = ((A003415(n)/gcd(n, A003415(n))) >= (A276086(n)/gcd(n, A276086(n))));

%Y Cf. A003415, A083345, A276086, A351251.

%Y Subsequences: A002110 (after its two initial terms), A369959, A369960.

%Y Cf. also A351228.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 07 2024