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%I #8 Jul 22 2022 16:45:30
%S 1,6,14,15,24,35,42,56,105,168,210,286,376,470,552,637,672,715,840,
%T 858,874,969,1144,1274,1288,1410,1848,1880,2001,2002,2145,2185,2261,
%U 2622,3021,3185,3290,3296,3375,3432,3496,3822,4290,4669,4830,4968,5005,5096,5640,6118,6291,6555,6783,7049,7776,8008,9555,9888
%N Numbers k such that A003973(k) is a multiple of A000203(k).
%C If both x and y are terms and gcd(x, y) = 1, then x*y is a term also.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); Select[Range[10^4], # == 1 || Divisible[Times @@ f @@@ FactorInteger[#], DivisorSigma[1, #]] &] (* _Amiram Eldar_, Jul 22 2022 *)
%o (PARI)
%o A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
%o A355940(n) = !(A003973(n)%sigma(n));
%o isA355941(n) = A355940(n);
%Y Cf. A000203, A003973.
%Y Positions of 1's in A355934, and also in A355940 (characteristic function).
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 22 2022
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