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%I #28 Dec 06 2020 17:10:30
%S 5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,46,47,49,
%T 51,53,55,57,59,61,65,67,69,71,73,77,79,81,83,85,87,89,91,93,95,97,99,
%U 101,103,105,106,107,109,111,113,115,117,118,119,121,123
%N Numbers m such that sigma(m) <= sigma(m-1).
%C This sequence is infinite because all primes p >= 5 are terms with sigma(p) < sigma(p-1).
%C The integer m is a term iff A053222(m-1) <= 0.
%C The numbers m such that sigma(m) = sigma(m-1) are in A231546.
%D J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 620 pp. 82, 280, Ellipses Paris 2004
%e Sigma(9) = 1+3+9 = 13 < sigma(8) = 1+2+4+8 = 15 so 9 is a term.
%e Sigma(15) = 1+3+5+15 = 24 = sigma(14) = 1+2+7+14 = 24 so 15 is a term.
%e Sigma(63) = 1+3+7+9+21+63 = 104 > sigma(62) = 1+2+31+62 = 96 and 63 is not a term.
%p filter:= m -> sigma(m) <= sigma(m-1): select(filter, [$1..500]);
%t Select[Range[2, 123], DivisorSigma[1, #] <= DivisorSigma[1, # - 1] &] (* _Amiram Eldar_, Mar 06 2020 *)
%t Flatten[Position[Partition[DivisorSigma[1,Range[200]],2,1],_?(#[[2]]<= #[[1]]&),1,Heads->False]]+1 (* _Harvey P. Dale_, Mar 28 2020 *)
%o (PARI) isok(m) = (m>1) && (sigma(m) <= sigma(m-1)); \\ _Michel Marcus_, Mar 09 2020
%Y Cf. A000203, A053222, A231546 (subsequence: sigma(m) = sigma(m-1)).
%Y Cf. A053224 (sigma(m) < sigma(m+1)), A053226 (sigma(m) > sigma(m+1)).
%K nonn
%O 1,1
%A _Bernard Schott_, Mar 06 2020
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