A186644 The sum of the oex divisors of n.

1, 3, 4, 5, 6, 12, 8, 15, 10, 18, 12, 26, 14, 24, 24, 25, 18, 36, 20, 40, 32, 36, 24, 60, 26, 42, 40, 54, 30, 72, 32, 59, 48, 54, 48, 80, 38, 60, 56, 90, 42, 96, 44, 82, 75, 72, 48, 118, 50, 88, 72, 96, 54, 120, 72, 120, 80, 90, 60, 166, 62, 96, 101, 117, 84, 144, 68, 124, 96, 144, 72, 186, 74, 114, 119, 138, 96

Offset: 1

Author

Vladimir Shevelev, Feb 25 2011

Keywords

• nonn

Comments

See A186643 for a definition of which divisors of n are classified as oex divisors.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A186643, A000203, A049417, A050376.

Programs

Maple

maxval := proc(n,d) local nshf,a ; if n mod d <> 0 then 0; else nshf := n ; a := 0 ; while nshf mod d = 0 do nshf := nshf /d ; a := a+1 ; end do: a; end if; end proc:
A186644 := proc(n) a := 1 ; for d in numtheory[divisors](n) minus {1} do if type(maxval(n,d),'odd') then a := a+d ; end if; end do: a ; end proc: # R. J. Mathar, Mar 04 2011

Mathematica

Table[DivisorSum[n, # &, Or[# == 1, OddQ@ IntegerExponent[n, #]] &], {n, 77}] (* Michael De Vlieger, Nov 23 2017 *)

PARI

a(n) = sumdiv(n, d, d*((d==1) || (valuation(n, d) % 2))); \\ Michel Marcus, Feb 06 2016

Formula

a(n) >= A049417(n).

Extensions

More terms from Antti Karttunen, Nov 23 2017