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

1,8

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

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

Mathematica

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

Prog

(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)));

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.

Sequence in context: A334108 A332813 A323077 * A257400 A328081 A194853

Adjacent sequences: A334198 A334199 A334200 * A334202 A334203 A334204

Keyword

nonn

Author

Antti Karttunen, May 11 2020

Status

approved