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A355596
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Numbers all of whose divisors are alternating numbers (A030141).
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3
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 32, 36, 41, 43, 47, 49, 50, 54, 58, 61, 63, 67, 69, 81, 83, 87, 89, 94, 98, 101, 103, 107, 109, 123, 125, 127, 129, 141, 145, 147, 149, 161, 163, 167, 181, 183, 189, 214, 218, 250, 254, 290, 298
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OFFSET
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1,2
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COMMENTS
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The smallest alternating number that is not a term is 30, because of 15.
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LINKS
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EXAMPLE
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32 is a term since all the divisors of 32, i.e., 1, 2, 4, 8, 16 and 32, are alternating numbers
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MATHEMATICA
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q[n_] := AllTrue[Divisors[n], !MemberQ[Differences[Mod[IntegerDigits[#], 2]], 0] &]; Select[Range[300], q] (* Amiram Eldar, Jul 12 2022 *)
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PROG
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(Python)
from sympy import divisors
def p(d): return 0 if d in "02468" else 1
def c(n):
if n < 10: return True
s = str(n)
return all(p(s[i]) != p(s[i+1]) for i in range(len(s)-1))
def ok(n):
return c(n) and all(c(d) for d in divisors(n, generator=True))
(PARI) isokd(n, d=digits(n))=for(i=2, #d, if((d[i]-d[i-1])%2==0, return(0))); 1; \\ A030141
isok(m) = sumdiv(m, d, isokd(d)) == numdiv(m); \\ Michel Marcus, Jul 12 2022
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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