A377377 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A377377

a(n) is the quotient of the practical number A005153(n) divided by its largest divisor that is primitive practical.

1, 1, 2, 1, 4, 2, 8, 3, 1, 4, 1, 1, 16, 6, 2, 1, 8, 9, 2, 2, 32, 1, 12, 1, 4, 2, 1, 3, 16, 5, 1, 18, 4, 4, 3, 64, 2, 1, 24, 5, 2, 8, 27, 4, 2, 6, 32, 7, 3, 10, 1, 2, 1, 36, 1, 8, 1, 3, 8, 6, 128, 1, 3, 9, 1, 1, 2, 48, 7, 10, 1, 1, 1, 3, 16, 54, 1, 8, 1, 1, 1, 4, 12, 1, 1, 9, 1, 64, 1, 14, 6, 20, 2, 1, 4, 2, 72, 2, 16, 15, 2, 1, 1, 1, 6, 1, 16, 81, 1, 25, 12

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Every practical number > 1 contains at least one primitive practical divisor because they are all even and 2 is primitive practical. Also 1 is primitive practical. If the largest primitive practical factor of the practical number A005153(n) is p then a(n)*p = A005153(n). Whenever a(n) = 1, A005153(n) is also primitive practical.

LINKS

Frank M Jackson, Table of n, a(n) for n = 1..10000

EXAMPLE

a(13) = 16 because the practical number A005153(13) = 32 = 2*16 and 2 is its largest primitive practical factor.

a(14) = 6 because the practical number A005153(14) = 36 = 6*6 and 6 is its largest primitive practical factor.

MATHEMATICA

lst1=Last/@ReadList["https://oeis.org/A267124/b267124.txt", {Number, Number}]; lst2=Last/@ReadList["https://oeis.org/A005153/b005153.txt", {Number, Number}]; getm[p_] := Module[{plst=Select[lst1, #<=p &], k, l, n=0}, l=Length@plst; If[Last@plst==p, Return[1]]; While[!IntegerQ[k=p/plst[[l-n]]], n++]; k]; Table[getm[lst2[[n]]], {n, 1, 100}]

CROSSREFS

Cf. A005153, A267124.

Sequence in context: A113418 A117000 A082392 * A233327 A307107 A085086

Adjacent sequences: A377365 A377366 A377367 * A377378 A377379 A377380

KEYWORD

nonn

AUTHOR

Frank M Jackson, Oct 26 2024

STATUS

approved