A328116 Numbers n such that the k-th arithmetic derivative of A276086(n) is zero for some k.

0, 1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 20, 21, 28, 30, 31, 32, 33, 35, 37, 38, 40, 43, 46, 47, 49, 50, 60, 61, 65, 67, 68, 71, 73, 74, 76, 79, 84, 85, 87, 91, 97, 98, 104, 106, 112, 118, 119, 121, 129, 133, 134, 151, 153, 180, 183, 196, 207, 210, 211, 212, 213, 218, 220, 221, 223, 225, 226, 227, 228, 229, 231, 235, 239, 240

Offset

1,3

Comments

Numbers x such that A276086(x) [which is A351255(a(x))] is in A099308.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, First 105368 terms (from 0 to 9699690)

Formula

For all n >= 1, A328307(a(n)) = n.

Prog

(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
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; };
isA099308(n) = { while(n>1, n = A003415checked(n)); (n); };
isA328116(n) = isA099308(A276086(n));

Crossrefs

Cf. A002110 (subsequence), A003415, A099308, A276086, A327969, A328306 (characteristic function), A328307 (its partial sums).

Cf. A351255 [= A276086(a(n))], A351256 [= A328114(a(n))].

Sequence in context: A059759 A042952 A126327 * A193286 A098132 A017900

Adjacent sequences: A328113 A328114 A328115 * A328117 A328118 A328119

Keyword

nonn

Author

Antti Karttunen, Oct 08 2019

Status

approved