cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A282843 #11 Apr 11 2025 03:27:46
%S A282843 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,
%T A282843 58,59,64,65,70,71,76,79,81,82,87,88,91,94,95,96,101,102,107,111,112,
%U A282843 115,118,119,125,128,129,130,132,137,141,142,143,144,149,152,155
%N A282843 Numbers k for which id(k) = id(k + id(k)), where id(k) = A037445(k) is the number of infinitary divisors of k.
%C A282843 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,...).
%H A282843 Charles R Greathouse IV, <a href="/A282843/b282843.txt">Table of n, a(n) for n = 1..10000</a>
%t A282843 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 *)
%o A282843 (PARI) id(n)=2^vecsum(apply(hammingweight, factor(n)[,2]))
%o A282843 is(n)=my(i=id(n)); id(n+i)==i \\ _Charles R Greathouse IV_, Feb 22 2017
%Y A282843 Cf. A037445, A050376, A175304.
%K A282843 nonn
%O A282843 1,1
%A A282843 _Vladimir Shevelev_, Feb 22 2017
%E A282843 More term from _Peter J. C. Moses_, Feb 22 2017