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

6, 30, 32, 36, 60, 210, 212, 213, 214, 216, 240, 420, 2310, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2322, 2324, 2328, 2340, 2342, 2343, 2344, 2346, 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

Offset

1,1

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..11643 (terms up to 3*A002110(9))

Victor Ufnarovski and Bo Åhlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003, #03.3.4.

Index entries for sequences related to primorial base

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA351228(n) = (A003415(n)>=A276086(n));

Crossrefs

Cf. A003415, A024451, A048103, A060735, A235991, A276085, A276086, A327862, A351088, A351089, A351232, A369656, A369663, A369664, A371104.

Union of A370127 and A370128.

Subsequence of A328118.

Subsequences: A351229, A369959, A369960, A369970 (after its two initial terms).

Cf. also A369650.

Sequence in context: A068510 A147798 A351226 * A369958 A197880 A175497

Adjacent sequences: A351225 A351226 A351227 * A351229 A351230 A351231

Keyword

nonn,base

Author

Antti Karttunen, Feb 05 2022

Status

approved