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 A192180 Composite numbers n such that all digits of n occur in its list of primes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Klaus Brockhaus, Table of n, a(n) for n = 1..10000 EXAMPLE 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). 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 *) PROG (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 CROSSREFS Cf. A037276. Sequence in context: A369342 A368873 A074237 * A134217 A039552 A063371 Adjacent sequences: A192177 A192178 A192179 * A192181 A192182 A192183 KEYWORD nonn,base AUTHOR Gil Broussard, Jun 24 2011 STATUS approved

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Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)