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

Author

Jonathan Vos Post, Sep 26 2010

Keywords

• nonn

Comments

54, 56, 87, and 95 are the smallest four numbers whose sum of divisors is the same hexagonal number (120).

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

Cf. A000203, A000384.

Numbers whose sum of divisors is a ...: A045746 (triangular number), A006532 (square), A180929 (pentagonal number).

Programs

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

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

Formula

A000203(a(n)) is in A000384.

Extensions

Corrected and extended by several authors, Sep 27 2010