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A355543 Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If k is an odd term > 1 then 2*k is also in the sequence.
LINKS
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 06 2022
STATUS
approved

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Last modified March 3 14:01 EST 2024. Contains 370512 sequences. (Running on oeis4.)