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A335272
For m to be a term there must exist three Euclidean divisions of m by d, d', and d", m = d*q + r = d'*q' + r' = d"*q" + r", such that (r, q, d), (r', d', q'), and (q", r", d") are three geometric progressions.
1
110, 132, 1332, 6162, 10712, 12210, 35156, 60762, 67340, 152490, 296480, 352242, 354620, 357006, 648830, 771762, 932190, 1197930, 2057790, 2803950, 3241800, 3310580, 4458432, 6454140, 7865220, 9613100, 10814232, 13976382, 16382256, 19267710, 53824232, 55138050
OFFSET
1,1
COMMENTS
Inspired by Project Euler, Problem 141 (see link).
The terms are necessary oblong numbers >= 6.
EXAMPLE
For 110:
110 | 18 110 | 6 110 | 100
----- ------ ---------
2 | 6 , 2 | 18 , 10 | 1
For 132, see A335065.
For 1332:
1332 | 121 1332 | 11 1332 | 1296
------ ------- -------
1 | 11 , 1 | 121 , 36 | 1 .
MATHEMATICA
Select[(#^2 + #) & /@ Range[2000], (n = #; AnyTrue[ Range[1 + Sqrt@ n], #^2 == Mod[n, #] Floor[n/#] &]) &] (* Giovanni Resta, Jun 03 2020 *)
PROG
(PARI) isob(n) = my(m=sqrtint(n)); m*(m+1)==n; \\ A002378
isgd(n) = {for(d=1, n, if((n\d)*(n%d)==d^2, return(1))); return(0)}; \\ A127629
isok(n) = isob(n) && isgd(n); \\ Michel Marcus, May 30 2020
CROSSREFS
Intersection of A127629 and A002378.
Sequence in context: A039447 A345386 A095611 * A358255 A307534 A200070
KEYWORD
nonn
AUTHOR
Bernard Schott, May 30 2020
EXTENSIONS
More terms from Michel Marcus, May 30 2020
a(18)-a(26) from Jinyuan Wang, May 30 2020
Terms a(27) and beyond from Giovanni Resta, Jun 03 2020
STATUS
approved