A229022 a(n) = sopf(n) + n/rad(n).

1, 3, 4, 4, 6, 6, 8, 6, 6, 8, 12, 7, 14, 10, 9, 10, 18, 8, 20, 9, 11, 14, 24, 9, 10, 16, 12, 11, 30, 11, 32, 18, 15, 20, 13, 11, 38, 22, 17, 11, 42, 13, 44, 15, 11, 26, 48, 13, 14, 12, 21, 17, 54, 14, 17, 13, 23, 32, 60, 12, 62, 34, 13, 34, 19, 17, 68, 21, 27, 15

Offset

1,2

Comments

a(n) is the sum of the main divisors of n because n = d_1*d_2*...*d_k*D where d_i are the distinct prime divisors of n and D = n/rad(n).

sopf(n) (A008472) is the sum of the distinct primes dividing n and rad(n) (A007947) is the product of the distinct primes dividing n.

If n is prime, then a(n) = sopf(n) + 1.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Maple

with(numtheory): a := proc(n) factorset(n):
convert(%, `+`) + n / convert(%, `*`) end:
seq(a(n), n=1..70); # Peter Luschny, Sep 19 2017

Mathematica

rad[n_]  := Times@@(First@#&/@FactorInteger@n); sopf[n_] := Plus@@(First@#&/@FactorInteger@n); Rest[Total[Transpose[sopf[#] + #/rad[#]&/@Range[100]]]]

Prog

(PARI) a(n) = my(f=factor(n)[, 1]); vecsum(f) + n/prod(k=1, #f, f[k]); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A007947, A008472.

Sequence in context: A323712 A215250 A354154 * A014683 A213222 A166737

Adjacent sequences: A229019 A229020 A229021 * A229023 A229024 A229025

Keyword

nonn

Author

Michel Lagneau, Sep 11 2013

Extensions

a(1) = 1 prepended by Peter Luschny, Sep 19 2017

Status

approved