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 A100007 Number of unitary divisors of 2n-1 (d such that d divides 2n-1, GCD(d,(2n-1)/d)=1). Bisection of A034444. 2
 1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 8, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 2, 8, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..105. FORMULA From Ilya Gutkovskiy, Apr 28 2017: (Start) a(n) = [x^(2*n-1)] Sum_{k>=1} mu(k)^2*x^k/(1 - x^k). a(n) = 2^omega(2*n-1). (End) From Amiram Eldar, Jan 28 2023: (Start) a(n) = A034444(2*n-1) = A068068(2*n-1). Sum_{k=1..n} a(k) ~ 4*n*((log(n) + 2*gamma - 1 + 7*log(2)/3 - 2*zeta'(2)/zeta(2)) / Pi^2, where gamma is Euler's constant (A001620). (End) EXAMPLE a(13)=2 because among the three divisors of 25 only 1 and 25 are unitary. MAPLE with(numtheory): for n from 1 to 120 do printf(`%d, `, 2^nops(ifactors(2*n-1)[2])) od: # Emeric Deutsch, Dec 24 2004 MATHEMATICA a[n_] := 2^PrimeNu[2*n-1]; Array[a, 100] (* Amiram Eldar, Jan 28 2023 *) PROG (PARI) a(n) = 2^omega(2*n-1); \\ Amiram Eldar, Jan 28 2023 CROSSREFS Cf. A001620, A034444, A068068, A100008. Sequence in context: A083261 A003648 A003642 * A104369 A051702 A073130 Adjacent sequences: A100004 A100005 A100006 * A100008 A100009 A100010 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 20 2004 EXTENSIONS More terms from Emeric Deutsch, Dec 24 2004 STATUS approved

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Last modified February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)