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A361255
Triangle read by rows: row n lists the exponential unitary divisors of n.
2
1, 2, 3, 2, 4, 5, 6, 7, 2, 8, 3, 9, 10, 11, 6, 12, 13, 14, 15, 2, 16, 17, 6, 18, 19, 10, 20, 21, 22, 23, 6, 24, 5, 25, 26, 3, 27, 14, 28, 29, 30, 31, 2, 32, 33, 34, 35, 6, 12, 18, 36, 37, 38, 39, 10, 40, 41, 42, 43, 22, 44, 15, 45, 46, 47, 6, 48, 7, 49, 10, 50, 51, 26, 52, 53, 6, 54, 55, 14, 56, 57, 58, 59
OFFSET
1,2
COMMENTS
Starts to differ from A322791 in row n=16, where 4 is an exponential divisor but not an exponential unitary divisor.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..15331 (first 10000 rows, flattened)
Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.
MAPLE
A361255 := proc(n)
local expundivs , d, isue, p, ai, bi;
expudvs := {} ;
for d in numtheory[divisors](n) do
isue := true ;
for p in numtheory[factorset](n) do
ai := padic[ordp](n, p) ;
bi := padic[ordp](d, p) ;
if bi > 0 then
if modp(ai, bi) <>0 or igcd(bi, ai/bi) <> 1 then
isue := false;
end if;
else
isue := false ;
end if;
end do;
if isue then
expudvs := expudvs union {d} ;
end if;
end do:
sort(expudvs) ;
end proc:
seq(op(A361255(n)), n=1..60) ;
MATHEMATICA
udivQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m] && CoprimeQ[m, n/m]);
expuDivQ[n_, d_] := Module[{f = FactorInteger[n]}, And @@ MapThread[udivQ, {f[[;; , 2]], IntegerExponent[d, f[[;; , 1]]]}]]; expuDivs[1] = {1};
expuDivs[n_] := Module[{d = Rest[Divisors[n]]}, Select[d, expuDivQ[n, #] &]];
Table[expuDivs[n], {n, 1, 70}] // Flatten (* Amiram Eldar, Mar 11 2023 *)
CROSSREFS
Cf. A322857 (row sums), A278908 (row lengths), A322791 (includes non-unitary exp divs).
Sequence in context: A369609 A284318 A322791 * A304745 A353853 A365384
KEYWORD
nonn,tabf
AUTHOR
R. J. Mathar, Mar 06 2023
STATUS
approved