A050414 -id:A050414 - cp's OEIS frontend

A322162 Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

80, 104, 832, 1952, 7424, 62464, 522752, 8382464, 33357824, 134193152, 267649024, 17167286272, 549754241024

Offset: 1

Amiram Eldar, Nov 29 2018

The bi-unitary version of A088831.

If m is a term of A050414, i.e., 2^m - 3 is prime, then 2^(2*m-2) * (2^m-3) is in this sequence, and also 2^(m-1) * (2^m-3) if m is even.

			80 is in this sequence since its sum of bi-unitary divisors is 162 = 2 * 80 + 2.

Cf. A050414, A088831, A188999.

fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; Select[Range[2,10000], Times@@(fun @@@ FactorInteger[#]) == 2#+2 &]

bsigma(n,f=factor(n))=prod(i=1,#f~, my(p=f[i,1], e=f[i, 2]); if (e%2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)));
forfactored(n=1,10^8, if(bsigma(n[1],n[2])==2*n[1]+2, print1(n[1]", "))) \\ Charles R Greathouse IV, Nov 29 2018

a(13) from Giovanni Resta, Dec 01 2018

A344516 Numbers k such that (2^k-5, 2^k-3) are twin primes.

Original entry on oeis.org

3, 4, 6, 10, 12, 20, 150

Offset: 1

Amiram Eldar, May 21 2021

No more terms <= A050414(66) = 2086750.

			3 is a term since (2^3-5, 2^3-3) = (3, 5) are twin primes.

G. L. Honaker, Jr. and Chris K. Caldwell, Prime Curios! 150.

Intersection of A050414 and A059608.

Cf. A001097.

Select[Range[150], And @@ PrimeQ[2^# - {3,5}] &]

A379806 Numbers k such that 2^prime(k) - 3 is prime.

Original entry on oeis.org

2, 3, 10, 51, 4462, 6883

Offset: 1

N. J. A. Sloane, Feb 01 2025

			Prime(3) = 5 and 2^5 - 3 = 29 is prime, so k = 3 is a member.

Cf. A000720, A050414, A283266.

isok(k) = ispseudoprime(1<Jinyuan Wang, Feb 09 2025

Apply PrimePi to A283266.

cp's OEIS Frontend

A322162 Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

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A344516 Numbers k such that (2^k-5, 2^k-3) are twin primes.

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A379806 Numbers k such that 2^prime(k) - 3 is prime.

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