A355596 Numbers all of whose divisors are alternating numbers (A030141).

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

Offset

1,2

Comments

The smallest alternating number that is not a term is 30, because of 15.

Links

Table of n, a(n) for n=1..62.

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

Subsequence of A030141.

Cf. A355593, A355594, A355595.

Similar sequences: A062687, A190217, A329419, A337941.

Sequence in context: A292514 A030141 A242367 * A246077 A064915 A375969

Adjacent sequences: A355593 A355594 A355595 * A355597 A355598 A355599

Keyword

nonn,base

Author

Bernard Schott, Jul 12 2022

Extensions

a(51) and beyond from Michael S. Branicky, Jul 12 2022

Status

approved