The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A352047 Sum of the divisor complements of the odd proper divisors of n. 11
 0, 2, 3, 4, 5, 8, 7, 8, 12, 12, 11, 16, 13, 16, 23, 16, 17, 26, 19, 24, 31, 24, 23, 32, 30, 28, 39, 32, 29, 48, 31, 32, 47, 36, 47, 52, 37, 40, 55, 48, 41, 64, 43, 48, 77, 48, 47, 64, 56, 62, 71, 56, 53, 80, 71, 64, 79, 60, 59, 96, 61, 64, 103, 64, 83, 96, 67, 72, 95, 96, 71, 104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n * Sum_{d|n, d=2} k * x^k / (1 - x^(2*k)). - Ilya Gutkovskiy, May 14 2023 exp( 2*Sum_{n>=1} a(n)*x^n/n ) is the g.f. of A300415. - Paul D. Hanna, May 15 2023 From Amiram Eldar, Oct 13 2023: (Start) a(n) = A000593(n) * A006519(n) - A000035(n). Sum_{k=1..n} a(k) = c * n^2 / 2, where c = Pi^2/8 = 1.23370055... (A111003). (End) EXAMPLE a(10) = 12; a(10) = 10 * Sum_{d|10, d<10, d odd} 1 / d = 10 * (1/1 + 1/5) = 12. MAPLE A352047 := proc(n) local a, d ; a := 0 ; for d in numtheory[divisors](n) do if type(d, 'odd') and d < n then a := a+n/d ; end if; end do: a ; end proc: seq(A352047(n), n=1..30) ; # R. J. Mathar, Mar 09 2022 MATHEMATICA Table[n DivisorSum[n, 1/# &, # < n && OddQ[#] &], {n, 72}] (* Michael De Vlieger, Mar 02 2022 *) a[n_] := DivisorSigma[-1, n / 2^IntegerExponent[n, 2]] * n - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *) PROG (PARI) a(n) = n*sumdiv(n, d, if ((d%2) && (d> valuation(n, 2), -1) - n % 2; \\ Amiram Eldar, Oct 13 2023 (Python) from math import prod from sympy import factorint def A352047(n): return prod(p**e if p == 2 else (p**(e+1)-1)//(p-1) for p, e in factorint(n).items()) - n % 2 # Chai Wah Wu, Mar 02 2022 CROSSREFS Cf. A000035, A000593, A002131, A006519, A111003, A300415. Sum of the k-th powers of the divisor complements of the odd proper divisors of n for k=0..10: A091954 (k=0), this sequence (k=1), A352048 (k=2), A352049 (k=3), A352050 (k=4), A352051 (k=5), A352052 (k=6), A352053 (k=7), A352054 (k=8), A352055 (k=9), A352056 (k=10). Sequence in context: A326066 A080785 A319605 * A245822 A357260 A069797 Adjacent sequences: A352044 A352045 A352046 * A352048 A352049 A352050 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Mar 01 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)