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

Author

Antti Karttunen, Oct 08 2019

Keywords

• nonn

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)

Crossrefs

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

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

Programs

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));

Formula

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