login
A328249
Numbers k such that the third arithmetic derivative of A276086(k) is prime.
2
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
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))));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 11 2019
STATUS
approved