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

1,1

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

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(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));

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.

Sequence in context: A318589 A132630 A033946 * A189710 A024678 A265384

Adjacent sequences: A328229 A328230 A328231 * A328233 A328234 A328235

Keyword

nonn

Author

Antti Karttunen, Oct 09 2019

Status

approved