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

1,2

Comments

Normal undulating integers are in A355301.

Links

Table of n, a(n) for n=1..100.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A355301, A355303, A355304.

Sequence in context: A095048 A332268 A355593 * A084302 A289872 A301855

Adjacent sequences: A355299 A355300 A355301 * A355303 A355304 A355305

Keyword

nonn,base

Author

Bernard Schott, Jun 29 2022

Status

approved