A361255 Triangle read by rows: row n lists the exponential unitary divisors of n.

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)

Nicuşor 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: A322791 A383761 A383760 * A304745 A353853 A365384

Adjacent sequences: A361252 A361253 A361254 * A361256 A361257 A361258

Keyword

nonn,tabf

Author

R. J. Mathar, Mar 06 2023

Status

approved