A192180 Composite numbers n such that all digits of n occur in its list of primes.

95, 132, 272, 312, 322, 326, 333, 731, 735, 912, 973, 995, 1111, 1212, 1255, 1292, 1972, 2112, 2132, 2232, 2272, 2512, 2672, 2737, 2994, 3171, 3192, 3210, 3212, 3243, 3315, 3393, 3792, 3933, 4172, 4341, 4371, 4383, 5150, 5192, 5271, 6973, 7132, 7210

Offset: 1

Author

Gil Broussard, Jun 24 2011

Keywords

• nonn
• base

Comments

For the purpose here, if a number has repeated prime factors, those are written repeatedly. For example, the factorization of 27 is expressed as (3, 3, 3) rather than (3^3). - Alonso del Arte, Jul 05 2011

Examples

			Since the prime factorization of 95 is (5, 19), and both 9 and 5 occur in (5, 19), the number 95 is on the list.
Since the prime factorization of 1255 is (5, 251), and 1, 2, and both 5s occur in (5, 251), the number 1255 is on the list.
22 is not on the list because its prime factorization is (2, 11) and that does not have enough 2s. Nor is 25 on the list because for this sequence we express its factorization as (5, 5) rather than (5^2).
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037276.

Programs

Magma

S:=[]; for n in [1..10000] do if not IsPrime(n) then u:=Intseq(n); f:=Factorization(n); v:=&cat[ [ f[j, 1]: i in [1..f[j, 2]] ]: j in [1..#f] ]; w:=&cat[ Intseq(p): p in v ]; if forall{ a: a in [0..9] | Multiplicity(SequenceToMultiset(u), a) le Multiplicity(SequenceToMultiset(w), a) } then Append(~S, n); end if; end if; end for; S; // Klaus Brockhaus, Jul 09 2011

Mathematica

Select[Range[2, 5000], Not[PrimeQ[#]] && Sort[DigitCount[FromDigits[Flatten[IntegerDigits/@Flatten[Table[#1, {#2}]&@@@FactorInteger[#]]]]] - DigitCount[#]][[1]] >= 0 &] (* Alonso del Arte, Jun 28 2011, based on HomePrimeStep function by Eric W. Weisstein *)