A180930 Numbers whose sum of divisors is a hexagonal number.
1, 5, 8, 12, 36, 54, 56, 87, 95, 160, 212, 328, 342, 356, 427, 531, 660, 672, 843, 852, 858, 909, 910, 940, 992, 1002, 1012, 1162, 1222, 1245, 1353, 1417, 1435, 1495, 1509, 1547, 1757, 1837, 1909, 1927, 1998, 2072, 2274, 2793, 2983, 3051, 3212, 3219, 3515, 3548, 3870
Offset: 1
Keywords
Examples
a(1) = 1 because the sum of divisors of 1 is the hexagonal number 1. a(2) = 5 because the sum of divisors of 5 is the hexagonal number 6. a(3) = 8 because the sum of divisors of 8 is the hexagonal number 15. a(4) = 12 because the sum of divisors of 12 is the hexagonal number 28.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
isA000384 := proc(n) if not issqr(8*n+1) then false; else sqrt(8*n+1)+1 ; (% mod 4) = 0 ; end if; end proc: for n from 1 to 4000 do if isA000384(numtheory[sigma](n)) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Sep 26 2010
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Mathematica
hnos=Table[n (2n-1),{n,500}]; okQ[n_]:=Module[{ds=DivisorSigma[1,n]},MemberQ[hnos,ds]] Select[Range[5000],okQ] (* Harvey P. Dale, Sep 26 2010 *) -
PARI
is(n)=ispolygonal(sigma(n),6) \\ Jason Yuen, Oct 14 2024
Extensions
Corrected and extended by several authors, Sep 27 2010
Comments