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 A059975 a(n) is the least number of prime factors (counted with multiplicity) of any integer with n divisors. 8
 1, 2, 2, 4, 3, 6, 3, 4, 5, 10, 4, 12, 7, 6, 4, 16, 5, 18, 6, 8, 11, 22, 5, 8, 13, 6, 8, 28, 7, 30, 5, 12, 17, 10, 6, 36, 19, 14, 7, 40, 9, 42, 12, 8, 23, 46, 6, 12, 9, 18, 14, 52, 7, 14, 9, 20, 29, 58, 8, 60, 31, 10, 6, 16, 13, 66, 18, 24, 11, 70, 7, 72, 37, 10, 20, 16, 15, 78, 8, 8, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS n*a(n) is the number of complex multiplications needed for the fast Fourier transform of n numbers, writing n = r1 * r2 where r1 is a prime. This sequence with offset 1,3 and a(1) = 0 is completely additive with a(p^e) = e*(p-1) for prime p and e >= 0. - Werner Schulte, Feb 23 2019 REFERENCES H. S. Wilf, Algorithms and complexity, Internet Edition, Summer, 1994, p. 56. LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..1000 K. V. Lever, Problem 89-11: The complexity of the standard form of an integer, SIAM Rev. 31 (3) (1989) 493-498. H. S. Wilf, Algorithms and complexity, Internet Edition, 1994, p. 56. FORMULA a(n) = sum ( a_i * (p_i - 1) ) where n = product ( p_i^a_i ) is the canonical factorization of n. a(n) = min(A001222(x): A000005(x)=n). a(n) = row sums of A138618 - row products of A138618. [Mats Granvik, May 23 2013] a(n) = A001414(n) - A001222(n). - David James Sycamore, Jul 17 2019 EXAMPLE a(18) = 5 since 18 = 2*3^2, a(18) = 1*(2-1) + 2*(3-1) = 5. MAPLE A059975 := proc(n)         local a, pf, p, e ;         a := 0 ;         for pf in ifactors(n) do                 p := op(1, pf) ;                 e := op(2, pf) ;                 a := a+e*(p-1) ;         end do:         a ; end proc: # R. J. Mathar, Oct 17 2011 MATHEMATICA Table[Total[(First /@ FactorInteger[n] - 1) Last /@ FactorInteger[n]], {n, 2, 100}] (* Danny Marmer, Nov 13 2014 - adapted to the offset by Vincenzo Librandi, Nov 13 2014 *) CROSSREFS Cf. A001222, A000005. Same as A087656 apart from offset. Cf. A001414, A001222. - David James Sycamore, Jul 17 2019 Sequence in context: A076435 A257010 A156864 * A087656 A122811 A089173 Adjacent sequences:  A059972 A059973 A059974 * A059976 A059977 A059978 KEYWORD nonn AUTHOR Yong Kong (ykong(AT)curagen.com), Mar 05 2001 EXTENSIONS Definition revised by Hugo van der Sanden, May 21 2010 STATUS approved

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Last modified February 20 07:54 EST 2020. Contains 332069 sequences. (Running on oeis4.)