A001103 Numbers k such that (k / product of digits of k) is 1 or a prime.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 15, 24, 36, 115, 175, 212, 624, 735, 816, 1115, 1184, 1197, 1416, 2144, 3171, 3276, 3915, 6624, 7119, 8832, 9612, 11133, 11212, 11331, 12128, 12216, 12768, 13131, 21184, 21728, 24912, 31113, 31488, 32172, 32616, 35175

Offset: 1

Author

N. J. A. Sloane, Bill Moran (moran1(AT)llnl.gov)

Keywords

• nonn
• base
• nice

Comments

For terms > 10 the quotient (k / product of digits of k) is prime. - David A. Corneth, Mar 30 2021

Examples

			21728 is in the sequence as 21728/(2*1*7*2*8) = 97 which is prime. - _David A. Corneth_, Mar 30 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..12677 (terms <= 10^12; first 448 terms from Klaus Brockhaus)

Crossrefs

Cf. A007954, A066577.

Cf. A052382, A010051, A007602, A188642.

Programs

Haskell

a001103 n = a001103_list !! (n-1)
a001103_list = filter f a052382_list where
   f x = m == 0 && (x' == 1 || a010051 x' == 1) where
       (x',m) = divMod x $ a007954 x
-- Reinhard Zumkeller, Nov 02 2011

Magma

IsA001103:=func< n | p ne 0 and n mod p eq 0 and (q eq 1 or IsPrime(q)) where q is (p eq 0 select 0 else n div p) where p is &*Intseq(n) >; [ n: n in [1..40000] | IsA001103(n) ]; // Klaus Brockhaus, Jan 24 2011

Mathematica

okQ[n_] := Block[{p = Times @@ IntegerDigits[n]}, n == p || PrimeQ[n/p]]; Select[ Range[36000], okQ]
Select[Range[40000],FreeQ[IntegerDigits[#],0]&&!CompositeQ[#/Times@@IntegerDigits[#]]&] (* Harvey P. Dale, Mar 30 2024 *)

PARI

is(n) = { my(vp = vecprod(digits(n))); if(vp > 0, c = n/vp; if(denominator(c) == 1, if(c == 1 || isprime(c), return(1)))); 0} \\ David A. Corneth, Mar 30 2021