



4, 6, 10, 12, 14, 15, 16, 20, 21, 22, 26, 27, 28, 30, 33, 34, 35, 36, 38, 39, 42, 44, 46, 48, 50, 51, 52, 54, 55, 57, 58, 60, 62, 64, 65, 66, 68, 69, 70, 74, 76, 77, 78, 80, 82, 84, 85, 86, 87, 91, 92, 93, 94, 95, 99, 100, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 118, 119, 122, 123, 124, 129, 130, 132, 133
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OFFSET

1,1


COMMENTS

Numbers n for which A051903(A003415(n)) >= A051903(n), i.e., numbers such that taking their arithmetic derivative does not decrease their "degree", A051903, the maximal exponent in prime factorization.


LINKS

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


EXAMPLE

10 = 2*5 has maximal exponent (A051903) 1, and its arithmetic derivative A003415(10) = 2+5 = 7 also has maximal exponent 1, thus 10 is included in this sequence.
15 = 3*5 has maximal exponent 1, and its arithmetic derivative A003415(15) = 3+5 = 8 = 2^3 has maximal exponent 3, thus 15 is included in this sequence.
For 8 = 2^3, its arithmetic derivative A003415(8) = 12 = 2^2 * 3, and as 2 < 3 (highest exponent of 12 is less than that of 8), 8 is NOT included here, and from this we also see that A100716 is not a subsequence of this sequence.


PROG

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328311(n) = if(n<=1, 0, 1+(A051903(A003415(n))  A051903(n)));
isA328321(n) = (A328311(n)>0);


CROSSREFS

Cf. A003415, A051903, A100716, A328302, A328310, A328311.
Cf. A328320 (complement), A051674, A157037, A328304, A328305 (subsequences).
Sequence in context: A137877 A246022 A174240 * A287342 A309177 A163164
Adjacent sequences: A328318 A328319 A328320 * A328322 A328323 A328324


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 13 2019


STATUS

approved



