login
A159302
Numbers k such that the number of factors on both sides of the equation k + (k+1) = 2k+1 is the same.
0
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?
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
KEYWORD
base,easy,nonn
AUTHOR
J. M. Bergot, Apr 09 2009
EXTENSIONS
Corrected and extended by R. J. Mathar, Apr 10 2009
STATUS
approved