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A100364
Numbers n such that the numbers of divisors of n,n+1,n+2 and n+3 are k,2k,4k,8k respectively for some k.
5
613, 757, 997, 1237, 2917, 6133, 9853, 15733, 19477, 22501, 24421, 25237, 26293, 26437, 28117, 31477, 33301, 35317, 44101, 45061, 46357, 51637, 53077, 56701, 59221, 61653, 61717, 64381, 65917, 66853, 68583, 70501, 70887, 72901, 75133
OFFSET
1,1
LINKS
EXAMPLE
n=613,614,615,616 have 2,4,8,16 divisors respectively.
MATHEMATICA
d0[x_] :=DivisorSigma[0, x]; ta={{0}}; Do[g=n; s=d0[n]; s1=d0[n+1]; s2=d0[n+2]; s3=d0[n+3] If[Equal[s1, 2*s]&&Equal[s2, 4*s]&&Equal[s3, 8*s], ta=Append[ta, n]; Print[{n, s, s1, s2, s3}]], {n, 1, 1000000}]; {ta=Delete[ta, 1], g}
nd2Q[{a_, b_, c_, d_}]:={b, c, d}/a=={2, 4, 8}; Position[Partition[ DivisorSigma[ 0, Range[80000]], 4, 1], _?(nd2Q[#]&)]//Flatten (* Harvey P. Dale, Feb 25 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 19 2004
STATUS
approved