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 A189803 Composite numbers n such that n'' = n'-1 where n' and n'' are the first and the second arithmetic derivative of n. 0
 9, 185, 341, 377, 437, 9005, 30413, 33953, 41009, 51533, 82673, 92909, 103073, 126509, 143009, 165773, 181793, 184973, 191309, 228653, 231713, 246893, 291233, 311309, 316973, 319793, 329357, 353009, 358433, 374513, 398093, 405809, 431009, 460193, 467309 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence A189710 (n"=n'-1) includes all prime numbers because p'=1 and p" = 0. Composite numbers are not very frequent. Are all terms semiprimes? These terms appear to be p*q such that p+q is a term in A054377, which has solutions to the equation n' = n-1. - T. D. Noe, Apr 27 2011 LINKS Table of n, a(n) for n=1..35. EXAMPLE 9' = 6, 9''= 6'= 5, 9" = 9'- 1 -> 9 is in the sequence. PROG (PARI) ader(n) = my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1])); \\ A003415 isok(k) = if (!isprime(k), my(d=ader(k)); ader(d) == d - 1); \\ Michel Marcus, Mar 13 2023 CROSSREFS Cf. A002808, A003415, A054377, A068346, A189710. Sequence in context: A064332 A319798 A300598 * A216409 A171194 A196297 Adjacent sequences: A189800 A189801 A189802 * A189804 A189805 A189806 KEYWORD nonn AUTHOR Giorgio Balzarotti, Apr 27 2011 STATUS approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)