A351395 Sum of the divisors of n that are either squarefree, prime powers, or both.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 72, 32, 63, 48, 54, 48, 25, 38, 60, 56, 30, 42, 96, 44, 40, 33, 72, 48, 40, 57, 43, 72, 46, 54, 48, 72, 36, 80, 90, 60, 76, 62, 96, 41, 127, 84, 144, 68, 58, 96, 144, 72

Offset: 1

Author

Wesley Ivan Hurt, Feb 09 2022

Keywords

• nonn

Examples

			a(36) = 25; 36 has 4 squarefree divisors 1,2,3,6 (where the primes 2 and 3 are both squarefree and 1st powers of primes) and 2 (additional) divisors that are powers of primes, 2^2 and 3^2. The sum of the divisors is then 1+2+3+4+6+9 = 25.
		

Links

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

Crossrefs

Cf. A001221, A008683, A246655.

Sums of divisors: A048250 (squarefree), A023889 (prime powers), A008472 (prime).

Programs

Mathematica

Array[DivisorSum[#, #*Sign[MoebiusMu[#]^2 + Boole[PrimeNu[#] == 1]] &] &, 71] (* Michael De Vlieger, Feb 10 2022 *)

PARI

a(n) = sumdiv(n, d, if (issquarefree(d) || isprimepower(d), d)); \\ Michel Marcus, Feb 10 2022

Formula

a(n) = Sum_{d|n} d * sign(mu(d)^2 + [omega(d) = 1]).