A239220 Cubes that are not divisible by any of their nonzero digits.

27, 343, 6859, 24389, 50653, 79507, 97336, 205379, 300763, 456533, 493039, 636056, 704969, 2048383, 2924207, 3307949, 3869893, 4330747, 4657463, 4826809, 5735339, 6539203, 7645373, 7880599, 23639903, 26730899, 28934443, 30664297, 33698267, 38272753, 42508549

Offset: 1

Author

Colin Barker, Mar 12 2014

Keywords

• nonn
• base

Comments

Intersection of A000578 and A038772.

Sequence is infinite because it contains (2*10^k + 3)^3, for k>1 and k not of the form 6*h + 2. - Giovanni Resta, Mar 13 2014

Examples

			50653 is in the sequence because 37^3 = 50653 is not divisible by 3, 5 or 6.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A239219, A239221, A239222.

Cf. A000578, A038772.

Programs

Mathematica

ndnzdQ[n_]:=NoneTrue[n/Select[IntegerDigits[n],#!=0&],IntegerQ]; Select[ Range[ 400]^3,ndnzdQ] (* Harvey P. Dale, Jan 16 2022 *)

PARI

isOK(n) = my(v=vecsort(digits(n^3), , 8)); for(i=1+(v[1]==0), #v, if(n^3%v[i]==0, return(0))); 1
s=[]; for(n=1, 1000, if(isOK(n), s=concat(s, n^3))); s

Formula

a(n) = A239219(n)^3. - Michel Marcus, Mar 19 2014