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A264740 Sum of odd parts of divisors of n. 1
1, 2, 4, 3, 6, 8, 8, 4, 13, 12, 12, 12, 14, 16, 24, 5, 18, 26, 20, 18, 32, 24, 24, 16, 31, 28, 40, 24, 30, 48, 32, 6, 48, 36, 48, 39, 38, 40, 56, 24, 42, 64, 44, 36, 78, 48, 48, 20, 57, 62, 72, 42, 54, 80, 72, 32, 80, 60, 60, 72, 62, 64, 104, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(2^k) = k + 1, a(p^k) = sigma(p^k) = (p^(k+1)-1) / (p-1) for p > 2.

It is easy to show that a(n) is odd iff n is a square.

a(n) = sigma(n) for odd n, since any divisor of an odd number is odd.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

Divisors of 10 are 1, 2, 5, 10. The odd parts of these are 1, 1, 5, 5, so a(10) = 1+1+5+5 = 12.

MATHEMATICA

f[p_, e_] := If[p == 2, e + 1, (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Jun 30 2020 *)

PROG

(PARI) a(n)=my(k=valuation(n, 2)); sigma(n)\(2^(k+1)-1)*(k+1)

(Haskell)

a264740 = sum . map a000265 . a027750_row'

-- Reinhard Zumkeller, Nov 23 2015

CROSSREFS

Cf. A000593, A000265, A000203.

Cf. A027750.

Sequence in context: A280866 A280864 A266411 * A137621 A242705 A039864

Adjacent sequences:  A264737 A264738 A264739 * A264741 A264742 A264743

KEYWORD

nonn,mult

AUTHOR

Franklin T. Adams-Watters, Nov 22 2015

STATUS

approved

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Last modified September 24 10:57 EDT 2020. Contains 337317 sequences. (Running on oeis4.)