

A321788


Product of semiprime factors using lunar arithmetic.


0



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, 21, 15, 22, 23, 13, 31, 22, 15, 22, 33, 23, 22, 17, 111, 21, 31, 33, 17, 22, 33, 21, 111, 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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..77.
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, 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]
Caldwell and Honaker, Prime Curio for 58.


FORMULA

a(n) = A087062(A084126(n), A084127(n)).  Michel Marcus, Nov 20 2018


EXAMPLE

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


MATHEMATICA

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 *)


CROSSREFS

Cf. A001358, A087062, A084126, A084127.
Sequence in context: A153095 A254574 A239585 * A182093 A254618 A268672
Adjacent sequences: A321785 A321786 A321787 * A321789 A321790 A321791


KEYWORD

nonn,base


AUTHOR

G. L. Honaker, Jr., Nov 18 2018


STATUS

approved



