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A328116
Numbers n such that the k-th arithmetic derivative of A276086(n) is zero for some k.
12
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 08 2019
STATUS
approved