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

1,1

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

Prog

(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))));

Crossrefs

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

Sequence in context: A345645 A274535 A027184 * A110702 A141394 A127256

Adjacent sequences: A328246 A328247 A328248 * A328250 A328251 A328252

Keyword

nonn

Author

Antti Karttunen, Oct 11 2019

Status

approved