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A324371
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Product of all primes p dividing n such that the sum of the base p digits of n is less than p, or 1 if no such prime.
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14
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1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 1, 5, 13, 3, 7, 29, 15, 31, 2, 11, 17, 35, 3, 37, 19, 13, 5, 41, 7, 43, 11, 1, 23, 47, 1, 7, 5, 17, 13, 53, 3, 55, 7, 19, 29, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 23, 7, 71, 1, 73, 37, 5, 19, 77, 13, 79, 5, 3, 41, 83, 21
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OFFSET
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1,2
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COMMENTS
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Does not contain any elements of A324315, and thus none of the Carmichael numbers A002997.
See the section on Bernoulli polynomials in Kellner and Sondow 2019.
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LINKS
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FORMULA
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EXAMPLE
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For p = 2 and 3, the sum of the base p digits of 6 is 1+1+0 = 2 >= 2 and 2+0 = 2 < 3, respectively, so a(6) = 3.
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MAPLE
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f:= n -> convert(select(p -> convert(convert(n, base, p), `+`)<p,
numtheory:-factorset(n)), `*`):map(f, [$1..100]); # Robert Israel, Apr 26 2020
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MATHEMATICA
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SD[n_, p_] := If[n < 1 || p < 2, 0, Plus @@ IntegerDigits[n, p]];
LP[n_] := Transpose[FactorInteger[n]][[1]];
DD3[n_] := Times @@ Select[LP[n], SD[n, #] < # &];
Table[DD3[n], {n, 1, 100}]
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PROG
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(Python)
from math import prod
from sympy.ntheory import digits
from sympy import primefactors as pf
def a(n): return prod(p for p in pf(n) if sum(digits(n, p)[1:]) < p)
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CROSSREFS
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Cf. A002997, A007947, A144845, A195441, A324315, A324316, A324317, A324318, A324319, A324320, A324369, A324370, A324404, A324405.
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KEYWORD
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AUTHOR
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STATUS
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approved
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