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A050694 Composite numbers n such that all prime factors of n are a substring of n. 5
25, 32, 125, 128, 135, 175, 243, 250, 256, 324, 375, 432, 512, 625, 735, 875, 1024, 1250, 1352, 1372, 1593, 1675, 1715, 1792, 2048, 2176, 2304, 2500, 2510, 2560, 2570, 2744, 3072, 3087, 3125, 3375, 3645, 3675, 3792, 4232, 4375, 5120, 5210, 5230, 5832 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 150 terms from Lava)

Gil Broussard, Integers containing prime factors as substrings.

FORMULA

a(n) << n log n. - Charles R Greathouse IV, Jul 09 2015

EXAMPLE

1675 = 5*5*67 -> 167{5} and 1{67}5.

MATHEMATICA

d[n_]:=IntegerDigits[n]; t={}; Do[le1=Max@@Length/@(t1=d[First/@FactorInteger[n]]); t2=Flatten[Table[Partition[d[n], i, 1], {i, le1}], 1]; If[!PrimeQ[n]&&Complement[t1, t2]=={}, AppendTo[t, n]], {n, 20, 5850}]; t (* Jayanta Basu, May 31 2013 *)

PROG

(PARI) substr(m, n)=my(a=#Str(m), b=#Str(n)); for(i=0, a-b, if(valuation(m-n, 10)>=b, return(1)); m\=10); 0

is(n)=if(isprime(n)||n<9, return(0)); my(f=factor(n)[, 1]); for(i=1, #f, if(!substr(n, f[i]), return(0))); 1 \\ Charles R Greathouse IV, Jul 09 2015

CROSSREFS

Cf. A050695, A050696, A035140, A050697.

Sequence in context: A263029 A225418 A035140 * A107608 A219951 A209333

Adjacent sequences:  A050691 A050692 A050693 * A050695 A050696 A050697

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Aug 15 1999

STATUS

approved

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Last modified September 25 20:53 EDT 2018. Contains 315425 sequences. (Running on oeis4.)