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

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

A000203(a(n)) is in A000384.

Example

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.

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 *)

Prog

(PARI) is(n)=ispolygonal(sigma(n), 6) \\ Jason Yuen, Oct 14 2024

Crossrefs

Cf. A000203, A000384.

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

Sequence in context: A260966 A338547 A124434 * A185729 A164128 A259912

Adjacent sequences: A180927 A180928 A180929 * A180931 A180932 A180933

Keyword

nonn

Author

Jonathan Vos Post, Sep 26 2010

Extensions

Corrected and extended by several authors, Sep 27 2010

Status

approved