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A227240
Numbers n such that sigma(n) divides sigma(2*n) and sigma(2*n + 1).
1
1, 3, 5, 7, 11, 23, 29, 41, 53, 77, 83, 89, 103, 113, 131, 143, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 533, 593, 641, 653, 659, 667, 683, 719, 743, 761, 807, 809, 817, 911, 953, 1013, 1019, 1031, 1049, 1073, 1103, 1223, 1229, 1289, 1409
OFFSET
1,2
COMMENTS
Numbers such that 2*n and/or 2*n + 1 is also in the sequence: 1, 3, 5, 11, 41, 89, 179, 359, 509, 719, 743, ... (Cf. A007700).
LINKS
MATHEMATICA
Select[Range[1000], IntegerQ[DivisorSigma[1, 2#]/DivisorSigma[1, #]] && IntegerQ[DivisorSigma[1, 2# + 1]/DivisorSigma[1, #]] &] (* Alonso del Arte, Jul 15 2013 *)
Select[Range[1500], And@@Divisible[{DivisorSigma[1, 2#], DivisorSigma[1, 2#+1]}, DivisorSigma[1, #]]&] (* Harvey P. Dale, Feb 25 2016 *)
PROG
(PARI) isok(n) = my(sn=sigma(n)); !(sigma(2*n) % sn) && !(sigma(2*n+1) % sn); \\ Michel Marcus, Oct 02 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Jul 03 2013
STATUS
approved