A351229 Numbers k for which A003415(k) >= A276086(k) > k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

2349, 2376, 2400, 2552, 4656, 4680, 4832, 4860, 6936, 6960, 30056, 30080, 30100, 30150, 30256, 30282, 32382, 32384, 32562, 36960, 60080, 510568, 510592, 510996, 511020, 511152, 511176, 511200, 512940, 513096, 513120, 513252, 513272, 515172, 515196, 515352, 515376, 515552, 517448, 517472, 519750, 540636, 540660, 540792

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..44.

Index entries for sequences related to primorial base

Mathematica

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 *)

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

Crossrefs

Cf. A003415, A049345, A276086.

Intersection of A351227 and A351228.

Positions of ones in A351089.

Sequence in context: A216989 A281697 A045306 * A264943 A224684 A198047

Adjacent sequences: A351226 A351227 A351228 * A351230 A351231 A351232

Keyword

nonn,base

Author

Antti Karttunen, Feb 05 2022

Status

approved