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A333038
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Numbers m such that sigma(m) <= sigma(m-1).
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3
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5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 106, 107, 109, 111, 113, 115, 117, 118, 119, 121, 123
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OFFSET
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1,1
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COMMENTS
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This sequence is infinite because all primes p >= 5 are terms with sigma(p) < sigma(p-1).
The integer m is a term iff A053222(m-1) <= 0.
The numbers m such that sigma(m) = sigma(m-1) are in A231546.
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REFERENCES
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J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 620 pp. 82, 280, Ellipses Paris 2004
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LINKS
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EXAMPLE
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Sigma(9) = 1+3+9 = 13 < sigma(8) = 1+2+4+8 = 15 so 9 is a term.
Sigma(15) = 1+3+5+15 = 24 = sigma(14) = 1+2+7+14 = 24 so 15 is a term.
Sigma(63) = 1+3+7+9+21+63 = 104 > sigma(62) = 1+2+31+62 = 96 and 63 is not a term.
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MAPLE
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filter:= m -> sigma(m) <= sigma(m-1): select(filter, [$1..500]);
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MATHEMATICA
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Select[Range[2, 123], DivisorSigma[1, #] <= DivisorSigma[1, # - 1] &] (* Amiram Eldar, Mar 06 2020 *)
Flatten[Position[Partition[DivisorSigma[1, Range[200]], 2, 1], _?(#[[2]]<= #[[1]]&), 1, Heads->False]]+1 (* Harvey P. Dale, Mar 28 2020 *)
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PROG
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(PARI) isok(m) = (m>1) && (sigma(m) <= sigma(m-1)); \\ Michel Marcus, Mar 09 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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