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Product of semiprime factors using lunar arithmetic.
1

%I #27 Jul 03 2020 14:55:05

%S 2,2,3,2,2,3,3,11,5,12,11,12,5,12,13,22,7,13,11,13,22,21,13,23,22,11,

%T 21,15,22,23,13,31,22,15,22,33,23,22,17,111,21,31,33,17,22,33,21,111,

%U 25,22,31,22,33,23,22,113,33,22,31,35,111,22,33,101,27,41,102,111,31,102,43,31,102,33,113,112,45

%N Product of semiprime factors using lunar arithmetic.

%H Metin Sariyar, <a href="/A321788/b321788.txt">Table of n, a(n) for n = 1..10000</a>

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.8. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

%H Caldwell and Honaker, <a href="https://primes.utm.edu/curios/page.php?curio_id=33738">Prime Curio for 58</a>.

%F a(n) = A087062(A084126(n), A084127(n)). - _Michel Marcus_, Nov 20 2018

%e a(16)=22 because the 16th semiprime is 46 = 2*23. In lunar arithmetic the product becomes 22.

%t ladd[x_, y_] := FromDigits[MapThread[Max, IntegerDigits[#, 10, Max@ IntegerLength [{x, y}]] & /@ {x, y}]]; lmult[x_, y_] := Fold[ladd, 0, Table[10^i, {i, IntegerLength[y] - 1, 0, -1}]*FromDigits /@ Transpose@Partition[Min[##] & @@@ Tuples[IntegerDigits[{x, y}]], IntegerLength[y]]]; s={}; Do[If[PrimeOmega[n]==2, f=FactorInteger[n]; x=f[[1,1]]; y=n/x; m=lmult[x,y]; AppendTo[s, m]],{n,1,300}]; s (* _Amiram Eldar_, Nov 19 2018 after _Davin Park_ at A087062 *)

%Y Cf. A001358, A087062, A084126, A084127.

%K nonn,base

%O 1,1

%A _G. L. Honaker, Jr._, Nov 18 2018