

A328116


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


11



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
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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



