A175508 a(n) is the difference of n and the product of the indices of prime factors of n with multiplicity, a(1) = 0.

1, 1, 1, 3, 2, 4, 3, 7, 5, 7, 6, 10, 7, 10, 9, 15, 10, 14, 11, 17, 13, 17, 14, 22, 16, 20, 19, 24, 19, 24, 20, 31, 23, 27, 23, 32, 25, 30, 27, 37, 28, 34, 29, 39, 33, 37, 32, 46, 33, 41, 37, 46, 37, 46, 40, 52, 41, 48, 42, 54, 43, 51, 47, 63, 47, 56, 48, 61, 51, 58, 51, 68, 52, 62

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 03 2010

Keywords

• nonn

Comments

Original name: If p is the product of k1-th prime, k2-th prime,..,kr-th prime then set a(n)=n-k1*k2*..*kr, if p is the k-th prime then set=n-k, a(1)=1 by convention. - Michael De Vlieger, Oct 23 2023

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003963.

Programs

Mathematica

Array[# - Times @@ PrimePi@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, 74] (* Michael De Vlieger, Oct 23 2023 *)

Formula

a(n) = n - A003963(n) for n>1.

Extensions

a(34) corrected by Georg Fischer, Dec 11 2022

Name edited by Michael De Vlieger, Oct 23 2023