A355302 a(n) is the number of normal undulating integers that divide n.
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 1, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 2, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 2, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 3, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 2, 8, 4, 4, 2, 12, 2, 4, 6, 7, 4, 4, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 2, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 4, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 3, 8
Offset: 1
Examples
44 has 6 divisors: {1, 2, 4, 11, 22, 44} of which 3 are not normal undulating integers: {11, 22, 44}, hence a(44) = 6 - 3 = 3.
Programs
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Mathematica
nuQ[n_] := AllTrue[(s = Sign[Differences[IntegerDigits[n]]]), # != 0 &] && AllTrue[Differences[s], # != 0 &]; a[n_] := DivisorSum[n, 1 &, nuQ[#] &]; Array[a, 100] (* Amiram Eldar, Jun 29 2022 *)
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PARI
isok(m) = if (m<10, return(1)); my(d=digits(m), dd = vector(#d-1, k, sign(d[k+1]-d[k]))); if (#select(x->(x==0), dd), return(0)); my(pdd = vector(#dd-1, k, dd[k+1]*dd[k])); #select(x->(x>0), pdd) == 0; \\ A355301 a(n) = sumdiv(n, d, isok(d)); \\ Michel Marcus, Jun 30 2022
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