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 A325817 a(n) is the least k >= 0 such that n-k and n-(sigma(n)-k) are relatively prime. 11
 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 27, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 0, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 1, 0, 1, 2, 5, 0, 0, 2, 0, 0, 1, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) is the least k >= 0 such that -n + k and (n-sigma(n))+k are coprime. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A000203(n) - A325818(n) = A001065(n) - A325826(n) = n - A325976(n). For all n: a(A000396(n)) = A000396(n)-1. a(n) <= n-1. a(n) <= A325965(n). a(n) <= A325967(n). EXAMPLE For n=15, gcd(15-0, 15-(24-0)) = 3, gcd(15-1, 15-(24-1)) = 2 and gcd(15-2, 15-(24-2)) = 1, thus a(15) = 2. PROG (PARI) A325817(n) = { my(s=sigma(n)); for(k=0, s, if(1==gcd(-n + k, (n-s)+k), return(k))); }; (PARI) A325817(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(i))); }; CROSSREFS Cf. A000203, A000396, A001065, A009194, A014567 (positions of zeros), A324213, A325818, A325826, A325962, A325965, A325967, A325976. Sequence in context: A106222 A090750 A324656 * A325967 A229656 A216722 Adjacent sequences:  A325814 A325815 A325816 * A325818 A325819 A325820 KEYWORD nonn AUTHOR Antti Karttunen, May 29 2019 STATUS approved

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Last modified July 29 08:46 EDT 2021. Contains 346340 sequences. (Running on oeis4.)