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 A362059 Total number of even divisors of all positive integers <= n. 2
 0, 1, 1, 3, 3, 5, 5, 8, 8, 10, 10, 14, 14, 16, 16, 20, 20, 23, 23, 27, 27, 29, 29, 35, 35, 37, 37, 41, 41, 45, 45, 50, 50, 52, 52, 58, 58, 60, 60, 66, 66, 70, 70, 74, 74, 76, 76, 84, 84, 87, 87, 91, 91, 95, 95, 101, 101, 103, 103, 111, 111, 113, 113, 119, 119, 123, 123, 127, 127, 131, 131, 140, 140, 142, 142, 146 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Convolved with A002865 gives A066898. LINKS Table of n, a(n) for n=1..76. FORMULA a(2n-1) = A006218(n-1), n >= 1. a(2n) = A006218(n), n >= 1. MATHEMATICA d[n_] := (e = IntegerExponent[n, 2]) * DivisorSigma[0, n/2^e]; Accumulate@ Array[d, 100] (* Amiram Eldar, Apr 07 2023 *) PROG (Python) from math import isqrt def A362059(n): return -(q:=isqrt(m:=n>>1))**2+(sum(m//k for k in range(1, q+1))<<1) # Chai Wah Wu, Apr 26 2023 CROSSREFS Partial sums of A183063. Cf. A000005, A002865, A006218, A066898, A060831, A271342. Sequence in context: A046200 A308415 A063281 * A117772 A026924 A240313 Adjacent sequences: A362056 A362057 A362058 * A362060 A362061 A362062 KEYWORD nonn,easy AUTHOR Omar E. Pol, Apr 06 2023 STATUS approved

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Last modified September 13 04:25 EDT 2024. Contains 375859 sequences. (Running on oeis4.)