cp's OEIS Frontend

A351228 Numbers k for which A003415(k) >= A276086(k), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%I A351228 #70 Mar 25 2024 21:29:08
%S A351228 6,30,32,36,60,210,212,213,214,216,240,420,2310,2312,2313,2314,2315,
%T A351228 2316,2317,2318,2319,2320,2322,2324,2328,2340,2342,2343,2344,2346,
%U A351228 2348,2349,2352,2370,2372,2376,2400,2520,2522,2523,2524,2526,2528,2550,2552,2730,4620,4622,4623,4624,4626,4628,4632,4650,4652,4656
%N A351228 Numbers k for which A003415(k) >= A276086(k), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
%C A351228 Conjecture: Apart from the initial 6, the rest of terms are the numbers k for which A003415(k) > A276086(k), thus giving the positions of zeros in A351232. In other words, it seems that only k=6 satisfies A003415(k) = A276086(k). See also comments in A351088.
%H A351228 Antti Karttunen, <a href="/A351228/b351228.txt">Table of n, a(n) for n = 1..11643 (terms up to 3*A002110(9))</a>
%H A351228 Victor Ufnarovski and Bo Åhlander, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html">How to Differentiate a Number</a>, J. Integer Seqs., Vol. 6, 2003, #03.3.4.
%H A351228 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A351228 (PARI)
%o A351228 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351228 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351228 isA351228(n) = (A003415(n)>=A276086(n));
%Y A351228 Cf. A003415, A024451, A048103, A060735, A235991, A276085, A276086, A327862, A351088, A351089, A351232, A369656, A369663, A369664, A371104.
%Y A351228 Union of A370127 and A370128.
%Y A351228 Subsequence of A328118.
%Y A351228 Subsequences: A351229, A369959, A369960, A369970 (after its two initial terms).
%Y A351228 Cf. also A369650.
%K A351228 nonn,base
%O A351228 1,1
%A A351228 _Antti Karttunen_, Feb 05 2022