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A351808
a(n) is the quotient obtained when pod(m) divides pod(m^2), with pod = product of digits = A007954 and m = A351807(n).
2
1, 2, 3, 2, 3, 3, 2, 8, 18, 4, 10, 3, 2, 8, 32, 15, 6, 21, 9, 14, 18, 0, 0, 6, 12, 21, 24, 0, 0, 0, 0, 0, 0, 0, 0, 7, 32, 81, 0, 10, 4, 0, 30, 35, 0, 21, 144, 0, 64, 32, 0, 2, 0, 0, 0, 12, 80, 252, 243, 12, 60, 27, 48, 256, 15, 30, 140, 36, 8, 14, 336, 96, 144
OFFSET
1,2
COMMENTS
a(n) = 0 iff m = A351807(n) is a term of A134844.
As pod(m) is 7-smooth number and pod(m^2) can be 0 (see example), all terms of the sequence are in {0} union A002473. The smallest term k such that the corresponding quotient = 0 or A002473(n) is A351809(n).
EXAMPLE
A351807(9) = 13, then pod(13) = 1*3 = 3 while pod(13^2) = pod(169) = 1*6*9 = 54; hence, a(9) = 54/3 = 18.
A351807(23) = 33, then pod(33) = 3*3 = 9 while pod(33^2) = pod(1089) = 1*0*8*9 = 0; hence, a(23) = 0.
MATHEMATICA
pod[n_] := Times @@ IntegerDigits[n]; r[n_] := If[(p = pod[n]) > 0, pod[n^2]/p, 1/2]; Select[r /@ Range[200], IntegerQ] (* Amiram Eldar, Feb 21 2022 *)
PROG
(PARI) lista(nn) = {my(list=List()); for (m=1, nn, my(d=digits(m), q); if (vecmin(d) && denominator(q = vecprod(digits(m^2))/vecprod(d)) == 1, listput(list, q); ); ); Vec(list); } \\ Michel Marcus, Feb 21 2022
(Python)
from math import prod
from itertools import count, islice
def A351808_gen(): # generator of terms
return (q for q, r in (divmod(prod(int(d) for d in str(m**2)), prod(int(d) for d in str(m))) for m in count(1) if '0' not in str(m)) if r == 0)
A351808_list = list(islice(A351808_gen(), 20)) # Chai Wah Wu, Feb 25 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Feb 20 2022
EXTENSIONS
More terms from Amiram Eldar, Feb 21 2022
STATUS
approved