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%I #41 Mar 01 2019 10:52:41
%S 1,350,6497,12317,133787,181427,404471,439097,485237,501182,549378,
%T 1410119,2696807,6220607,6827369,6954767,9770027,10302419,10449347,
%U 10887977,11014007,16745387,18959111,25883519,27334469,39508037,40311149,40551617,42561437,44592209
%N Numbers k such that (k, k+2) are not twin primes yet sigma(k+2)/d(k+2) - sigma(k)/d(k) = 1.
%C A variation of A050507 with average of the divisors instead of their sum.
%H Amiram Eldar, <a href="/A322668/b322668.txt">Table of n, a(n) for n = 1..241</a> (terms below 10^10)
%t f[n_] := DivisorSigma[1, n]/DivisorSigma[0, n]; aQ[n_] := f[n + 2] - f[n] == 1 && !(PrimeQ[n] && PrimeQ[n + 2]); Select[Range[1000000], aQ]
%o (PARI) isok(k) = !(isprime(k) && isprime(k+2)) && (sigma(k+2)/numdiv(k+2) - sigma(k)/numdiv(k) == 1); \\ _Michel Marcus_, Jan 22 2019
%Y Cf. A000005 (number of divisors), A000203 (sum of divisors).
%Y Cf. A050507, A056774, A057020, A057021, A238380.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jan 11 2019
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