A328249 Numbers k such that the third arithmetic derivative of A276086(k) is prime.

5, 15, 21, 31, 43, 79, 91, 98, 104, 106, 223, 229, 231, 254, 255, 289, 291, 301, 305, 423, 453, 456, 487, 670, 674, 677, 692, 702, 730, 736, 2343, 2378, 2380, 2400, 2409, 2534, 2537, 2543, 2552, 2562, 2585, 2602, 2618, 2629, 2767, 2804, 2821, 2831, 2839, 2942, 2943, 2957, 2962, 2963, 2974, 4621, 4669, 4672, 4687, 4717, 4841, 4844

Offset: 1

Author

Antti Karttunen, Oct 11 2019

Keywords

• nonn

Comments

Numbers k such that A003415(A003415(A327860(k))) = A099306(A276086(k)) is a prime.

Numbers k such that A276086(k) is in A328239.

For all n, A327969(a(n)) <= 6. This is sharp for example with a(7) = 91.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1315

Crossrefs

Cf. A003415, A099306, A276086, A327860, A327969, A328239, A328233, A328240.

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); };
isA328249(n) = isprime(A003415(A003415(A327860(n))));