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Numbers k such that the product of the digits of k equals the number of divisors of k.
3

%I #11 Aug 14 2017 02:40:41

%S 1,2,14,22,24,32,42,116,122,126,141,211,221,222,411,512,1114,1118,

%T 1128,1132,1141,1144,1218,1222,1242,1314,1332,1411,1611,1612,2111,

%U 2114,2132,2214,2232,2312,2511,3114,3211,3212,4116,4131,4312,6112,8211

%N Numbers k such that the product of the digits of k equals the number of divisors of k.

%H Giovanni Resta, <a href="/A074312/b074312.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 is a term as the product of the digits of 24 is 2*4 = 8 and the number of divisors = 8.

%p with(numtheory):l := 1:a[1] := 1:for n from 2 to 10000 do d := convert(n,base,10): if(product(d[i],i=1..nops(d))=tau(n)) then l := l+1:a[l] := n:fi:od:seq(a[i],i=1..l); # _Sascha Kurz_

%t Select[Range[10^4], Apply[Times, IntegerDigits[ # ]] == DivisorSigma[0, # ] &]

%Y Cf. A057531, A066613.

%K base,easy,nonn

%O 1,2

%A _Joseph L. Pe_, Sep 22 2002