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

Author

Antti Karttunen, Feb 05 2022

Keywords

• nonn
• base

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

• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A049345, A276086.

Intersection of A351227 and A351228.

Positions of ones in A351089.

Programs

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 *)

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)); };