cp's OEIS Frontend

A261778 Positive numbers n such that (digitsum(n))^2 equals (product of digits(n))^3.

%I A261778 #21 Sep 08 2022 08:46:13
%S A261778 1,11114,11141,11411,14111,41111,111122,111212,111221,112112,112121,
%T A261778 112211,121112,121121,121211,122111,211112,211121,211211,212111,
%U A261778 221111,1111111111111111119,1111111111111111191,1111111111111111911,1111111111111119111,1111111111111191111,1111111111111911111
%N A261778 Positive numbers n such that (digitsum(n))^2 equals (product of digits(n))^3.
%C A261778 Sequence is infinite because it contains all the numbers made of k fours and 8^k-4k ones. - _Giovanni Resta_, Sep 01 2015
%H A261778 Chai Wah Wu, <a href="/A261778/b261778.txt">Table of n, a(n) for n = 1..10000</a>
%H A261778 Charles R Greathouse IV, <a href="/A261778/a261778.txt">GP script</a>
%e A261778 11114 appears in the sequence because (1 + 1 + 1 + 1 + 4)^2 = (1*1*1*1*4)^3 = 64.
%e A261778 111122 appears in the sequence because (1 + 1 + 1 + 1 + 2 + 2)^2  = (1*1*1*1*2*2)^3 = 64.
%t A261778 Select[Range[20000000], Plus @@ IntegerDigits[#]^2 == Times @@ IntegerDigits[#]^3 &]
%o A261778 (PARI) for(n = 1,1000000, d = digits(n); if((sumdigits(n))^2 == prod(i = 1, #d, d[i])^3, print1(n, ", ")));
%o A261778 (PARI) proddigits(n)=my(d=digits(n)); prod(i=1,#d,d[i])
%o A261778 is(n)=my(s=sumdigits(n)); if(!ispower(s,3), return(0)); s^2==proddigits(n)^3 \\ _Charles R Greathouse IV_, Aug 31 2015
%o A261778 (Magma)  [n : n in [1..1000000] | (&+Intseq(n))^2 eq (&*Intseq(n))^3 ];
%Y A261778 Cf. A034710, A117720, A117723, A241846.
%K A261778 nonn,base
%O A261778 1,2
%A A261778 _K. D. Bajpai_, Aug 31 2015
%E A261778 a(22)-a(27) from _Charles R Greathouse IV_, Aug 31 2015