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A180930
Numbers whose sum of divisors is a hexagonal number.
2
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
Numbers whose sum of divisors is a ...: A045746 (triangular number), A006532 (square), A180929 (pentagonal number).
Sequence in context: A260966 A338547 A124434 * A185729 A164128 A259912
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Sep 26 2010
EXTENSIONS
Corrected and extended by several authors, Sep 27 2010
STATUS
approved