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A355036 a(n) is the least number whose product of digits in primorial base equals n.

%I A355036 #10 Jun 18 2022 08:41:42
%S A355036 0,1,5,21,17,159,23,1509,29,111,161,25659,83,392949,1511,171,89,
%T A355036 8711259,113,184837209,167,1521,25661,5141378799,119,1209,392951,741,
%U A355036 1517,187854439329,173,6224078222919,149,25671,8711261,1629,203,274774574506989,184837211
%N A355036 a(n) is the least number whose product of digits in primorial base equals n.
%C A355036 All terms except a(0) = 0 are odd.
%C A355036 Each prime number sets a new record.
%H A355036 Rémy Sigrist, <a href="/A355036/b355036.txt">Table of n, a(n) for n = 0..2356</a>
%H A355036 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A355036 A355037(a(n)) = n.
%F A355036 a(A005867(n)) = A057588(n) for any n > 0.
%e A355036 The first terms, alongside their primorial base expansion, are:
%e A355036   n   a(n)       pr(a(n))
%e A355036   --  ---------  ------------------
%e A355036    0          0                   0
%e A355036    1          1                   1
%e A355036    2          5                 2_1
%e A355036    3         21               3_1_1
%e A355036    4         17               2_2_1
%e A355036    5        159             5_1_1_1
%e A355036    6         23               3_2_1
%e A355036    7       1509           7_1_1_1_1
%e A355036    8         29               4_2_1
%e A355036    9        111             3_3_1_1
%e A355036   10        161             5_1_2_1
%e A355036   11      25659        11_1_1_1_1_1
%e A355036   12         83             2_3_2_1
%e A355036   13     392949      13_1_1_1_1_1_1
%o A355036 (PARI) a(n) = { if (n==0, 0, my (v=0, f=1); forprime (r=2, oo, forstep (d=r-1, 1, -1, if (n%d==0, v+=f*d; n/=d; break;);); if (n==1, return (v), f*=r))) }
%Y A355036 Cf. A005867, A057588, A263130 (factorial base analog), A355037.
%K A355036 nonn,base
%O A355036 0,3
%A A355036 _Rémy Sigrist_, Jun 16 2022