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.
%I A079067 #34 Apr 09 2024 08:06:41
%S A079067 0,0,1,0,2,0,3,0,1,1,4,0,5,2,1,0,6,0,7,1,2,3,8,0,2,4,1,2,9,0,10,0,3,5,
%T A079067 2,0,11,6,4,1,12,1,13,3,1,7,14,0,3,1,5,4,15,0,3,2,6,8,16,0,17,9,2,0,4,
%U A079067 2,18,5,7,1,19,0,20,10,1,6,3,3,21,1,1,11,22,1,5,12,8,3,23,0,4,7,9,13,6,0
%N A079067 Number of primes less than greatest prime factor of n but not dividing n.
%C A079067 For n >= 2, a(n) is the largest part minus the number of distinct parts of the partition having Heinz number n. The Heinz number of a partition [i_1, i_2, ..., i_r] is defined as Product_{j=1..r} (i_j-th prime) (concept used by _Alois P. Heinz_ in A215366 as an encoding of a partition). For example, for the partition [1, 1, 1, 4] we get 2*2*2*7 = 56; a(56) = 4 - #{1,4} = 2. - _Emeric Deutsch_, Jun 09 2015 [edited by _Peter Munn_, Apr 09 2024]
%H A079067 Alois P. Heinz, <a href="/A079067/b079067.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from G. C. Greubel)
%F A079067 a(n) = A049084(A006530(n)) - A001221(n) = A061395(n) - A001221(n).
%F A079067 a(n) = 0 iff n = m*prime(k)#, where prime(k)# is the k-th primorial (A002110(k)) and A006530(m) <= A000040(k).
%F A079067 a(A000040(k)) = k - 1.
%F A079067 a(n) = A001221(A083720(n)). - _Peter Munn_, Apr 09 2024
%p A079067 with(numtheory): a := proc (n) local B: B := proc (n) local nn, j, m: nn := op(2, ifactors(n)): for j to nops(nn) do m[j] := op(j, nn) end do: [seq(seq(pi(op(1, m[i])), q = 1 .. op(2, m[i])), i = 1 .. nops(nn))] end proc: max(B(n))-nops(convert(B(n), set)) end proc: 0, seq(a(n), n = 2 .. 96); # The subprogram B yields the partition having Heinz number n. # _Emeric Deutsch_, Jun 09 2015
%p A079067 # second Maple program:
%p A079067 with(numtheory):
%p A079067 a:= n-> (s-> pi(max(0, s))-nops(s))(factorset(n)):
%p A079067 seq(a(n), n=1..100); # _Alois P. Heinz_, Sep 03 2019
%t A079067 a[1] = 0; a[n_] := With[{fi = FactorInteger[n]}, PrimePi[fi][[-1, 1]] - Length[fi]]; Array[a, 100] (* _Jean-François Alcover_, Jan 08 2016 *)
%o A079067 (PARI) a(n) = if (n==1, 0, my(pf=factor(n)[,1]); primepi(vecmax(pf)) - #pf); \\ _Michel Marcus_, May 05 2017
%Y A079067 See the formula section for the relationships with A000040, A001221, A002110, A006530, A049084, A061395, A083720.
%Y A079067 Cf. A079068, A215366.
%K A079067 nonn,easy
%O A079067 1,5
%A A079067 _Reinhard Zumkeller_, Dec 20 2002