cp's OEIS Frontend

A180930 Numbers whose sum of divisors is a hexagonal number.

%I A180930 #18 Oct 15 2024 05:13:36
%S A180930 1,5,8,12,36,54,56,87,95,160,212,328,342,356,427,531,660,672,843,852,
%T A180930 858,909,910,940,992,1002,1012,1162,1222,1245,1353,1417,1435,1495,
%U A180930 1509,1547,1757,1837,1909,1927,1998,2072,2274,2793,2983,3051,3212,3219,3515,3548,3870
%N A180930 Numbers whose sum of divisors is a hexagonal number.
%C A180930 54, 56, 87, and 95 are the smallest four numbers whose sum of divisors is the same hexagonal number (120).
%H A180930 Charles R Greathouse IV, <a href="/A180930/b180930.txt">Table of n, a(n) for n = 1..10000</a>
%F A180930 A000203(a(n)) is in A000384.
%e A180930 a(1) = 1 because the sum of divisors of 1 is the hexagonal number 1.
%e A180930 a(2) = 5 because the sum of divisors of 5 is the hexagonal number 6.
%e A180930 a(3) = 8 because the sum of divisors of 8 is the hexagonal number 15.
%e A180930 a(4) = 12 because the sum of divisors of 12 is the hexagonal number 28.
%p A180930 isA000384 := proc(n) if not issqr(8*n+1) then false; else sqrt(8*n+1)+1 ; (% mod 4) = 0 ; end if; end proc:
%p A180930 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
%t A180930 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 *)
%o A180930 (PARI) is(n)=ispolygonal(sigma(n),6) \\ _Jason Yuen_, Oct 14 2024
%Y A180930 Cf. A000203, A000384.
%Y A180930 Numbers whose sum of divisors is a ...: A045746 (triangular number), A006532 (square), A180929 (pentagonal number).
%K A180930 nonn
%O A180930 1,2
%A A180930 _Jonathan Vos Post_, Sep 26 2010
%E A180930 Corrected and extended by several authors, Sep 27 2010