A322668 Numbers k such that (k, k+2) are not twin primes yet sigma(k+2)/d(k+2) - sigma(k)/d(k) = 1.

1, 350, 6497, 12317, 133787, 181427, 404471, 439097, 485237, 501182, 549378, 1410119, 2696807, 6220607, 6827369, 6954767, 9770027, 10302419, 10449347, 10887977, 11014007, 16745387, 18959111, 25883519, 27334469, 39508037, 40311149, 40551617, 42561437, 44592209

Offset: 1

Author

Amiram Eldar, Jan 11 2019

Keywords

• nonn

Comments

A variation of A050507 with average of the divisors instead of their sum.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..241 (terms below 10^10)

Crossrefs

Cf. A000005 (number of divisors), A000203 (sum of divisors).

Cf. A050507, A056774, A057020, A057021, A238380.

Programs

Mathematica

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]

PARI

isok(k) = !(isprime(k) && isprime(k+2)) && (sigma(k+2)/numdiv(k+2) - sigma(k)/numdiv(k) == 1); \\ Michel Marcus, Jan 22 2019