cp's OEIS Frontend

A180929 Numbers whose sum of divisors is a pentagonal number.

%I A180929 #28 Oct 20 2024 04:09:05
%S A180929 1,6,11,104,116,129,218,363,408,440,481,534,566,568,590,638,646,684,
%T A180929 718,807,895,979,999,1003,1007,1137,1251,1282,1557,1935,2197,2367,
%U A180929 2571,2582,2808,2855,3132,3283,3336,3578,3737,3891,3946,3980,4172,4484,4886,5158
%N A180929 Numbers whose sum of divisors is a pentagonal number.
%H A180929 Harvey P. Dale, <a href="/A180929/b180929.txt">Table of n, a(n) for n = 1..1000</a>
%F A180929 A000203(a(n)) is in A000326.
%e A180929 a(1) = 1 because the sum of divisors of 1 is the pentagonal number 1.
%e A180929 a(2) = 6 because the sum of divisors of 6 is the pentagonal number 12.
%e A180929 a(3) = 11 because the sum of divisors of 11 is the pentagonal number 12.
%e A180929 a(4) = 104 because the sum of divisors of 104 is the pentagonal number 210.
%e A180929 a(5) = 116 because the sum of divisors of 116 is the pentagonal number 210.
%e A180929 a(6) = 129 because the sum of divisors of 129 is the pentagonal number 176.
%e A180929 a(7) = 218 because the sum of divisors of 218 is the pentagonal number 330.
%p A180929 isA000326 := proc(n) if not issqr(24*n+1) then false; else sqrt(24*n+1)+1 ; (% mod 6) = 0 ; end if; end proc:
%p A180929 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
%t A180929 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 *)
%t A180929 Select[Range[5200],IntegerQ[(Sqrt[1+24DivisorSigma[1,#]]+1)/6]&] (* _Harvey P. Dale_, Jun 14 2013 *)
%o A180929 (PARI) is(n)=ispolygonal(sigma(n),5) \\ _Jason Yuen_, Oct 14 2024
%Y A180929 Cf. A000203, A000326.
%Y A180929 Numbers whose sum of divisors is a ...: A045746 (triangular number), A006532 (square), A180930 (hexagonal number).
%K A180929 easy,nonn
%O A180929 1,2
%A A180929 _Jonathan Vos Post_, Sep 25 2010
%E A180929 Corrected and extended by _R. J. Mathar_ and _Harvey P. Dale_, Sep 26 2010