%I #10 Feb 03 2019 09:39:58
%S 1,13,22,37,58,67,73,82,94,148,166,178,193,229,277,292,310,313,364,
%T 397,409,418,457,478,502,514,541,553,577,586,598,634,652,682,697,733,
%U 757,769,796,838,841,850,886,907,913,922,958,982,1018,1137,1138,1162,1174
%N Numbers k such that the number of factors on both sides of the equation k + (k+1) = 2k+1 is the same.
%C How often is one of k or k+1 a prime for any solution k?
%F Let npf(k) be the number of factors of k; for 36, npf(36)=4 since 36=2*2*3*3. The sequence lists numbers k such that npf(k) + npf(k+1) = npf(2k+1).
%e For k=58, 58 + 59 = 117, npf(58) + npf(59) = 2 + 1 = 3 = npf(117), so 58 is a term.
%p A001222 := proc(n) numtheory[bigomega](n) ; end:
%p isA159302 := proc(n) RETURN( A001222(n)+A001222(n+1) = A001222(2*n+1) ); end:
%p for n from 1 to 10000 do if isA159302(n) then printf("%d,",n) ; fi; od:
%p # _R. J. Mathar_, Apr 10 2009
%K base,easy,nonn
%O 1,2
%A _J. M. Bergot_, Apr 09 2009
%E Corrected and extended by _R. J. Mathar_, Apr 10 2009