A349910 a(n) = Sum_{d|n, d<n} A048673(d).

0, 1, 1, 3, 1, 6, 1, 8, 4, 7, 1, 19, 1, 9, 8, 22, 1, 27, 1, 23, 10, 10, 1, 56, 5, 12, 17, 31, 1, 47, 1, 63, 11, 13, 11, 93, 1, 15, 13, 69, 1, 65, 1, 35, 39, 18, 1, 165, 7, 43, 14, 43, 1, 128, 12, 95, 16, 19, 1, 160, 1, 22, 51, 185, 14, 74, 1, 47, 19, 80, 1, 288, 1, 24, 51, 55, 14, 92, 1, 205, 80, 25, 1, 226, 15, 27

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A336840(n) - A048673(n).

Mathematica

f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, s[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *)

Prog

(PARI)
A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A349910(n) = sumdiv(n, d, if(d==n, 0, A048673(d)));

Crossrefs

Cf. A048673, A336840.

Sequence in context: A336646 A336647 A336645 * A168111 A309491 A109646

Adjacent sequences: A349907 A349908 A349909 * A349911 A349912 A349913

Keyword

nonn

Author

Antti Karttunen, Dec 10 2021

Status

approved