A383428 Primitive terms in A066192: number k such that k is a term of A066192 and k/2 is not.

4, 12, 56, 120, 528, 672, 992, 1456, 2160, 2208, 6720, 9024, 9120, 11904, 13104, 16256, 17472, 24800, 29568, 55104, 55552, 73440, 90816, 95040, 119040, 120960, 121024, 123648, 131040, 146688, 151680, 174720, 195072, 223104, 297600, 397440, 399616, 445536, 505344

Offset: 1

Author

Amiram Eldar, Apr 27 2025

Keywords

• nonn

Comments

If a(1) = 1 instead of 4, then this will be the sequence of primitive terms in A069519.

If k is a term then 2^m * k is a term in A066192 for all m >= 0.

If there is an odd term in this sequence it must be an odd perfect number (A000396). See the comments in A066192.

Except for 4, numbers k such that A091570(k) | k and k/A091570(k) is odd.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..755 (terms below 10^11)
• Index entries for sequences where any odd perfect numbers must occur.

Crossrefs

Subsequence of A066191 and A066192.

Cf. A000396, A069519, A091570.

Programs

Mathematica

q[n_] := Module[{s = DivisorSigma[1, n/2^IntegerExponent[n, 2]] - If[OddQ[n], n, 0]}, Divisible[n, s] && OddQ[n/s]]; Select[Range[550000], # == 4 || (CompositeQ[#] && q[#]) &]

PARI

isok(k) = if(k == 1 || isprime(k), 0, if(k == 4, 1, my(s = sigma(k >> valuation(k, 2)) - if(k%2, k)); !(k % s) && (k/s) % 2));