A282843 Numbers k for which id(k) = id(k + id(k)), where id(k) = A037445(k) is the number of infinitary divisors of k.

2, 3, 5, 6, 7, 8, 9, 10, 11, 14, 17, 18, 22, 23, 28, 29, 32, 34, 35, 41, 44, 46, 47, 48, 51, 58, 59, 64, 65, 70, 71, 76, 79, 81, 82, 87, 88, 91, 94, 95, 96, 101, 102, 107, 111, 112, 115, 118, 119, 125, 128, 129, 130, 132, 137, 141, 142, 143, 144, 149, 152, 155

Offset: 1

Author

Vladimir Shevelev, Feb 22 2017

Keywords

• nonn

Comments

The infinitary analog of A175304. The sequence contains smaller of pairs(p,q) of terms of A050376 if q-p=2 (Fermi-Dirac twin primes). Unlike A175304, this sequence contains some squares (64,81,144,...).

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037445, A050376, A175304.

Programs

Mathematica

f[p_, e_] := 2^DigitCount[e, 2, 1]; id[1] = 1; id[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[200], id[#] == id[# + id[#]] &] (* Amiram Eldar, Apr 11 2025 *)

PARI

id(n)=2^vecsum(apply(hammingweight, factor(n)[,2]))
is(n)=my(i=id(n)); id(n+i)==i \\ Charles R Greathouse IV, Feb 22 2017

Extensions

More term from Peter J. C. Moses, Feb 22 2017