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 A195199 Smallest multiple of n with more than twice as many divisors as n. 4
 4, 12, 12, 24, 20, 36, 28, 48, 36, 60, 44, 120, 52, 84, 60, 96, 68, 144, 76, 120, 84, 132, 92, 240, 100, 156, 108, 168, 116, 180, 124, 192, 132, 204, 140, 360, 148, 228, 156, 240, 164, 252, 172, 264, 180, 276, 188, 480, 196, 300, 204, 312, 212, 432, 220, 336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = Min_{A000005(k*n) > 2*A000005(n)} k*n. EXAMPLE a(4) must have more than 6 divisors because 4 has 3 divisors and 3*2=6. Therefore, it cannot be 16 because 16 has only 5 divisors. MAPLE A195199 := proc(n)         for k from 2 do                 if numtheory[tau](k*n) > 2*numtheory[tau](n) then                         return k*n ;                 end if;         end do: end proc: # R. J. Mathar, Oct 21 2011 MATHEMATICA Table[d = DivisorSigma[0, n]; m = 1; While[DivisorSigma[0, m*n] <= 2*d, m++]; m*n, {n, 100}] (* T. D. Noe, Oct 21 2011 *) PROG (PARI) a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<=2*d, m+=n); m; \\ Michel Marcus, Jan 08 2022 (Python) from sympy import divisor_count def a(n):     dtarget, m = 2*divisor_count(n), 2*n     while divisor_count(m) <= dtarget: m += n     return m print([a(n) for n in range(1, 57)]) # Michael S. Branicky, Jan 08 2022 (Python) from math import prod from itertools import count from collections import Counter from sympy import factorint def A195199(n):     f = Counter(factorint(n))     d = prod(e+1 for e in f.values())     for m in count(2):         if prod(e+1 for e in (f+Counter(factorint(m))).values()) > 2*d:             return m*n # Chai Wah Wu, Feb 28 2022 CROSSREFS Cf. A000005. Sequence in context: A005886 A096442 A211437 * A294628 A323188 A284126 Adjacent sequences:  A195196 A195197 A195198 * A195200 A195201 A195202 KEYWORD nonn AUTHOR J. Lowell, Oct 12 2011 STATUS approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)