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 A328321 Numbers n for which A328311(n) = 1 + A051903(A003415(n)) - A051903(n) is strictly positive. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)