A334201 - OEIS

%I #23 Jan 01 2021 11:41:12

%S 0,0,0,1,0,1,0,2,2,1,0,2,0,1,2,3,0,3,0,2,2,1,0,3,3,1,4,2,0,3,0,4,2,1,

%T 3,4,0,1,2,3,0,3,0,2,4,1,0,4,4,4,2,2,0,5,3,3,2,1,0,4,0,1,4,5,3,3,0,2,

%U 2,4,0,5,0,1,5,2,4,3,0,4,6,1,0,4,3,1,2,3,0,5,4,2,2,1,3,5,0,5,4,5,0,3,0,3,5

%N a(n) = A056239(n) - A061395(n).

%C a(n) is the sum of all other parts of the partition having Heinz number n except one instance of the largest part.

%H Antti Karttunen, <a href="/A334201/b334201.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A056239(n) - A061395(n) = A056239(A052126(n)).

%F a(n) = A318995(A122111(n)).

%F a(n) = a(A064989(n)) + A001222(n) - 1.

%F a(n) = A339895(n) + A339896(n). - _Antti Karttunen_, Dec 31 2020

%t Array[Total[# /. {p_, c_} /; p > 0 :> PrimePi[p] c] - PrimePi@ #[[-1, 1]] &@ FactorInteger[#] &, 105] (* _Michael De Vlieger_, May 14 2020 *)

%o (PARI)

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A334201(n) = if(1==n,0,(bigomega(n)-1)+A334201(A064989(n)));

%Y Cf. A001222, A052126, A056239, A061395, A122111, A318995.

%Y Sum of A339895 and A339896.

%Y Differs from A323077 for the first time at n=169, where a(169) = 6, while A323077(169) = 5.

%Y Cf. also A334107.

%K nonn

%O 1,8

%A _Antti Karttunen_, May 11 2020