A328232 Numbers whose arithmetic derivative (A003415) is a primorial number, including cases where it is the first primorial, A002110(0) = 1.

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 161, 163, 167, 173, 179, 181, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317

Offset: 1

Author

Antti Karttunen, Oct 09 2019

Keywords

• nonn

Comments

Numbers n such that A327859(n) = A276086(A003415(n)) is a prime.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A003415, A024451 (arith. deriv. of primorials), A068346, A276086, A327859, A328233.

Union of A000040 and A327978 (gives the composite terms).

Differs from A189710 for the first time by having term a(39) = 161, which is not included in A189710, while A189710(44) = 185 is the first term in latter that is not included here.

Programs

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(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A327859(n) = A276086(A003415(n));
isA328232(n) = isprime(A327859(n));