A223456 Composite numbers whose number of proper divisors has a prime number of proper divisors.
16, 36, 48, 64, 80, 81, 100, 112, 120, 144, 162, 168, 176, 196, 208, 210, 216, 225, 256, 264, 270, 272, 280, 304, 312, 324, 330, 368, 378, 384, 390, 400, 405, 408, 440, 441, 456, 462, 464, 484, 496, 510, 512, 520, 546, 552, 567, 570, 576, 592, 594, 616, 625
Offset: 1
Examples
a(1) = 16, which has 4 proper divisors (1, 2, 4, 8). 4 has 2 proper divisors, 2 is prime. 2 steps were needed.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
a223456 n = a223456_list !! (n-1) a223456_list = filter ((== 1 ) . a010051 . a032741 . a032741) a002808_list -- Reinhard Zumkeller, Sep 22 2013
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Maple
isA223456 := proc(n) local npd ; if not isprime(n) and n >=4 then npd := A032741(n) ; if isprime( A032741(npd)) then true; else false; end if ; else false; end if; end proc: for n from 16 to 630 do if isA223456(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Sep 18 2013
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Mathematica
Select[Range[1000], PrimeQ[DivisorSigma[0, DivisorSigma[0, #] - 1] - 1] &] (* Alonso del Arte, Jul 21 2013 *)