A159302 Numbers k such that the number of factors on both sides of the equation k + (k+1) = 2k+1 is the same.

1, 13, 22, 37, 58, 67, 73, 82, 94, 148, 166, 178, 193, 229, 277, 292, 310, 313, 364, 397, 409, 418, 457, 478, 502, 514, 541, 553, 577, 586, 598, 634, 652, 682, 697, 733, 757, 769, 796, 838, 841, 850, 886, 907, 913, 922, 958, 982, 1018, 1137, 1138, 1162, 1174

Offset

1,2

Comments

How often is one of k or k+1 a prime for any solution k?

Links

Table of n, a(n) for n=1..53.

Formula

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).

Example

For k=58, 58 + 59 = 117, npf(58) + npf(59) = 2 + 1 = 3 = npf(117), so 58 is a term.

Maple

A001222 := proc(n) numtheory[bigomega](n) ; end:
isA159302 := proc(n) RETURN( A001222(n)+A001222(n+1) = A001222(2*n+1) ); end:
for n from 1 to 10000 do if isA159302(n) then printf("%d, ", n) ; fi; od:
# R. J. Mathar, Apr 10 2009

Crossrefs

Sequence in context: A164455 A164504 A162245 * A172187 A164412 A164472

Adjacent sequences: A159299 A159300 A159301 * A159303 A159304 A159305

Keyword

base,easy,nonn

Author

J. M. Bergot, Apr 09 2009

Extensions

Corrected and extended by R. J. Mathar, Apr 10 2009

Status

approved