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 A333038 Numbers m such that sigma(m) <= sigma(m-1). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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) <= 0. The numbers m such that sigma(m) = sigma(m-1) are in A231546. REFERENCES J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 620 pp. 82, 280, Ellipses Paris 2004 LINKS EXAMPLE 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. MAPLE filter:= m -> sigma(m) <= sigma(m-1): select(filter, [\$1..500]); MATHEMATICA Select[Range[2, 123], DivisorSigma[1, #] <= DivisorSigma[1, # - 1] &] (* Amiram Eldar, Mar 06 2020 *) Flatten[Position[Partition[DivisorSigma[1, Range], 2, 1], _?(#[]<= #[]&), 1, Heads->False]]+1 (* Harvey P. Dale, Mar 28 2020 *) PROG (PARI) isok(m) = (m>1) && (sigma(m) <= sigma(m-1)); \\ Michel Marcus, Mar 09 2020 CROSSREFS Cf. A000203, A053222, A231546 (subsequence: sigma(m) = sigma(m-1)). Cf. A053224 (sigma(m) < sigma(m+1)), A053226 (sigma(m) > sigma(m+1)). Sequence in context: A099047 A174392 A084926 * A049013 A267872 A062545 Adjacent sequences:  A333035 A333036 A333037 * A333039 A333040 A333041 KEYWORD nonn AUTHOR Bernard Schott, Mar 06 2020 STATUS approved

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Last modified September 20 01:14 EDT 2020. Contains 337229 sequences. (Running on oeis4.)