A355543 Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k.

1, 65, 130, 175, 260, 350, 525, 1050, 1105, 2100, 2210, 4420, 5425, 8840, 10850, 16275, 20737, 21700, 30225, 32045, 32550, 41474, 60450, 64090, 65100, 70525, 82948, 86025, 103685, 120900, 128180, 130200, 141050, 171275, 172050, 200725, 207370, 207553, 211575

Offset

1,2

Comments

If k is an odd term > 1 then 2*k is also in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

65 is a term since A050999(65) = 4420 = 65 * 68 is divisible by 65.

Mathematica

f[p_, e_] := If[p == 2, 1, (p^(2*e + 2) - 1)/(p^2 - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], Divisible[s[#], #] &]

Prog

(PARI) f(n) = sumdiv(n, d, if(d%2==1, d^2, 0 ) ); \\ A050999
isok(k) = !(f(k) % k); \\ Michel Marcus, Jul 07 2022

Crossrefs

Cf. A050999.

Similar sequences: A007691, A046762.

Sequence in context: A044569 A158071 A352982 * A348759 A357651 A294169

Adjacent sequences: A355540 A355541 A355542 * A355544 A355545 A355546

Keyword

nonn

Author

Amiram Eldar, Jul 06 2022

Status

approved