OFFSET
1,2
COMMENTS
The smallest alternating number that is not a term is 30, because of 15.
EXAMPLE
32 is a term since all the divisors of 32, i.e., 1, 2, 4, 8, 16 and 32, are alternating numbers
MATHEMATICA
q[n_] := AllTrue[Divisors[n], !MemberQ[Differences[Mod[IntegerDigits[#], 2]], 0] &]; Select[Range[300], q] (* Amiram Eldar, Jul 12 2022 *)
PROG
(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))
print([k for k in range(1, 200) if ok(k)]) # Michael S. Branicky, Jul 12 2022
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jul 12 2022
EXTENSIONS
a(51) and beyond from Michael S. Branicky, Jul 12 2022
STATUS
approved