cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A225230 In the canonical prime factorization of n: (number of distinct primes) minus (largest prime exponent).

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%I A225230 #12 Sep 09 2024 02:41:18
%S A225230 0,0,0,-1,0,1,0,-2,-1,1,0,0,0,1,1,-3,0,0,0,0,1,1,0,-1,-1,1,-2,0,0,2,0,
%T A225230 -4,1,1,1,0,0,1,1,-1,0,2,0,0,0,1,0,-2,-1,0,1,0,0,-1,1,-1,1,1,0,1,0,1,
%U A225230 0,-5,1,2,0,0,1,2,0,-1,0,1,0,0,1,2,0,-2,-3
%N A225230 In the canonical prime factorization of n: (number of distinct primes) minus (largest prime exponent).
%H A225230 Reinhard Zumkeller, <a href="/A225230/b225230.txt">Table of n, a(n) for n = 1..10000</a>
%F A225230 a(n) = A001221(n) - A051903(n).
%F A225230 a(A212164(n)) < 0; a(A212165(n)) <= 0; a(A212166(n)) = 0; a(A188654(n)) <> 0; a(A212167(n)) >= 0; a(A212168(n)) > 0.
%t A225230 a[n_] := Module[{e = FactorInteger[n][[;;, 2]]}, Length[e] - Max[e]]; Array[a, 100] (* _Amiram Eldar_, Sep 09 2024 *)
%o A225230 (Haskell)
%o A225230 a225230 n = a001221 n - a051903 n
%o A225230 (PARI) a(n) = if (n>1, my(f=factor(n)); #f~ - vecmax(f[,2]), 0); \\ _Michel Marcus_, Jan 26 2022
%Y A225230 Cf. A001221, A051903.
%Y A225230 Cf. A188654, A212164, A212165, A212166, A212167, A212168.
%K A225230 sign
%O A225230 1,8
%A A225230 _Reinhard Zumkeller_, May 03 2013