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 A354206 a(n) = A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse. 5
 1, 1, 1, 23, 3, 1, 1, 5, 11, 3, 2, 23, 1, 1, 3, 469, 2, 11, 1, 69, 1, 2, 1, 5, 53, 1, 4, 23, 11, 3, 7, 69, 2, 2, 3, 253, 3, 1, 1, 15, 1, 1, 1, 46, 33, 1, 2, 469, 33, 53, 2, 23, 23, 4, 6, 5, 1, 11, 13, 69, 29, 7, 11, 19507, 3, 2, 1, 46, 1, 3, 2, 55, 2, 3, 53, 23, 2, 1, 3, 1407, 2797, 1, 5, 23, 6, 1, 11, 10, 9, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 Index entries for sequences computed from indices in prime factorization Index entries for sequences related to sigma(n) FORMULA Multiplicative with a(p^e) = A354203((q^(e+1)-1)/(q-1)) where q = A354200(A000720(p)). a(n) = A354203(A354205(n)) = A354203(sigma(A354202(n))). a(n) = n - A354207(n). PROG (PARI) A354200(n) = if(1==n, 5, my(p=prime(n), m=p%4); forprime(q=1+p, , if(m==(q%4), return(q)))); A354201(n) = if(n<=3, (n+1)\2, my(m=prime(n)%4); forstep(i=n-1, 0, -1, if(m==(prime(i)%4), return(prime(i))))); A354202(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = A354200(primepi(f[k, 1]))); factorback(f); }; A354203(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = A354201(primepi(f[k, 1]))); factorback(f); }; A354206(n) = A354203(sigma(A354202(n))); CROSSREFS Cf. A000203, A000720, A354200, A354201, A354202, A354203, A354205, A354207. Cf. A354361 (positions of 1's). Cf. also A326042, A348750, A354088, A354096 for similar constructions. Sequence in context: A051313 A350201 A040518 * A040517 A040519 A040520 Adjacent sequences: A354203 A354204 A354205 * A354207 A354208 A354209 KEYWORD nonn,mult AUTHOR Antti Karttunen, May 23 2022 STATUS approved

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Last modified June 3 14:00 EDT 2023. Contains 363110 sequences. (Running on oeis4.)