A334201 a(n) = A056239(n) - A061395(n).

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 11 2020

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

Sum of A339895 and A339896.

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

Cf. also A334107.

Programs

Mathematica

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

PARI

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

Formula

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

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

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

a(n) = A339895(n) + A339896(n). - Antti Karttunen, Dec 31 2020