A180929 Numbers whose sum of divisors is a pentagonal number.
1, 6, 11, 104, 116, 129, 218, 363, 408, 440, 481, 534, 566, 568, 590, 638, 646, 684, 718, 807, 895, 979, 999, 1003, 1007, 1137, 1251, 1282, 1557, 1935, 2197, 2367, 2571, 2582, 2808, 2855, 3132, 3283, 3336, 3578, 3737, 3891, 3946, 3980, 4172, 4484, 4886, 5158
Offset: 1
Examples
a(1) = 1 because the sum of divisors of 1 is the pentagonal number 1. a(2) = 6 because the sum of divisors of 6 is the pentagonal number 12. a(3) = 11 because the sum of divisors of 11 is the pentagonal number 12. a(4) = 104 because the sum of divisors of 104 is the pentagonal number 210. a(5) = 116 because the sum of divisors of 116 is the pentagonal number 210. a(6) = 129 because the sum of divisors of 129 is the pentagonal number 176. a(7) = 218 because the sum of divisors of 218 is the pentagonal number 330.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Maple
isA000326 := proc(n) if not issqr(24*n+1) then false; else sqrt(24*n+1)+1 ; (% mod 6) = 0 ; end if; end proc: for n from 1 to 5000 do if isA000326(numtheory[sigma](n)) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Sep 26 2010
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Mathematica
pnos=Table[(n (3n-1))/2,{n,500}]; okQ[n_]:=Module[{ds=DivisorSigma[1,n]},MemberQ[pnos,ds]] Select[Range[5000],okQ] (* Harvey P. Dale, Sep 26 2010 *) Select[Range[5200],IntegerQ[(Sqrt[1+24DivisorSigma[1,#]]+1)/6]&] (* Harvey P. Dale, Jun 14 2013 *) -
PARI
is(n)=ispolygonal(sigma(n),5) \\ Jason Yuen, Oct 14 2024
Extensions
Corrected and extended by R. J. Mathar and Harvey P. Dale, Sep 26 2010