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A159302
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The sequence lists the n's such that the number of factors on both sides of the equation n + (n+1) = 2n+1` is the same.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is a preliminary proposal for further examination.
How often is one of n or n+1 a prime for any solution n?
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FORMULA
| Let npf(n) equal the number of factors of n; for 36 npf(36)=4 since 36=2*2*3*3. The sequence lists n such that npf(n) + npf(n+1) = npf(2n+1).
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EXAMPLE
| For 58 + 59 = 117, npf(58) + npf(59) = 2+1=3 = npf(117).
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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: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 10 2009]
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CROSSREFS
| Sequence in context: A164413 A164441 A162245 * A172187 A164412 A164472
Adjacent sequences: A159299 A159300 A159301 * A159303 A159304 A159305
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KEYWORD
| base,easy,nonn
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AUTHOR
| J. M. Bergot (thekingfishb(AT)yahoo.ca), Apr 09 2009
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 10 2009
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