A351229 - OEIS

%I #10 Feb 05 2022 17:20:12

%S 2349,2376,2400,2552,4656,4680,4832,4860,6936,6960,30056,30080,30100,

%T 30150,30256,30282,32382,32384,32562,36960,60080,510568,510592,510996,

%U 511020,511152,511176,511200,512940,513096,513120,513252,513272,515172,515196,515352,515376,515552,517448,517472,519750,540636,540660,540792

%N Numbers k for which A003415(k) >= A276086(k) > k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%C The terms appear to come in batches dictated by their primorial base expansion (A049345), these terms having only low digit values in that base.

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%t Select[Range[550000], Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] >= m > #] &] (* _Michael De Vlieger_, Feb 05 2022 *)

%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 isA351229(n) = { my(u=A276086(n)); ((u > n) && (A003415(n) >= u)); };

%Y Cf. A003415, A049345, A276086.

%Y Intersection of A351227 and A351228.

%Y Positions of ones in A351089.

%K nonn,base

%O 1,1

%A _Antti Karttunen_, Feb 05 2022