A328240 Numbers k such that the second arithmetic derivative of A276086(k) is prime.

4, 12, 32, 35, 40, 46, 47, 65, 67, 68, 71, 73, 74, 76, 220, 221, 225, 226, 227, 250, 256, 257, 276, 283, 284, 420, 421, 425, 426, 436, 486, 489, 494, 2324, 2325, 2352, 2370, 2387, 2525, 2530, 2531, 2555, 2560, 2565, 2566, 2583, 2596, 2734, 2739, 2760, 2765, 2769, 2771, 2773, 2795, 2797, 2798, 2803, 4623, 4627, 4628

Offset: 1

Author

Antti Karttunen, Oct 10 2019

Keywords

• nonn

Comments

Numbers k for which A003415(A327860(k)) = A003415(A003415(A276086(k))) is a prime.

Numbers k such that A276086(k) is in A192192, or equally, k such that A327860(k) is in A157037.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1217
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A157037, A192192, A276086, A327860, A327969, A328233.

Subsequence of A328116 and of A328242.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A327860(n) = { my(m=1, i=0, s=0, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), my(e=((n%nextpr)/pr)); m *= (prime(i)^e); s += (e / prime(i)); n-=(n%nextpr)); pr=nextpr); (s*m); };
isA328240(n) = isprime(A003415(A327860(n)));

Formula

For all n, a(A327969(n)) <= 5.