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%I #14 Mar 19 2022 06:32:31
%S 3,13,5,41,11,2479,23,73,103,2249,19,7177,211,691,3089,1289,53263,
%T 726493,41,1597,2243,64406,13129,31351,983,1579,197,43037,1411,
%U 38246575,389,3607,15403,61286,709,1638349,3587,16249,3585641,1017119,1292839,132347,593,32203,51963
%N a(n) is the least k such that A033273(k) is equal to (A033273(n*k + 1) - 1)/n where A033273(n) is the number of nonprime divisors of n.
%e a(2) = 13 because A033273(13) = (A033273(2*13 + 1) - 1)/2 = (A033273(27) - 1)/2 = 1.
%t f[n_] := DivisorSigma[0, n] - PrimeNu[n]; a[n_] := Module[{k = 2}, While[f[k] != (f[n*k + 1] - 1)/n, k++]; k]; Array[a, 29] (* _Amiram Eldar_, Mar 10 2022 *)
%o (PARI) f(n) = numdiv(n) - omega(n); \\ A033273
%o a(n) = my(k=2); while (f(k) != (f(n*k + 1) - 1)/n, k++); k; \\ _Michel Marcus_, Mar 10 2022
%Y Cf. A000005, A001221, A033273, A350516.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Mar 09 2022