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

1, 11114, 11141, 11411, 14111, 41111, 111122, 111212, 111221, 112112, 112121, 112211, 121112, 121121, 121211, 122111, 211112, 211121, 211211, 212111, 221111, 1111111111111111119, 1111111111111111191, 1111111111111111911, 1111111111111119111, 1111111111111191111, 1111111111111911111

Offset: 1

Author

K. D. Bajpai, Aug 31 2015

Keywords

• nonn
• base

Comments

Sequence is infinite because it contains all the numbers made of k fours and 8^k-4k ones. - Giovanni Resta, Sep 01 2015

Examples

			11114 appears in the sequence because (1 + 1 + 1 + 1 + 4)^2 = (1*1*1*1*4)^3 = 64.
111122 appears in the sequence because (1 + 1 + 1 + 1 + 2 + 2)^2  = (1*1*1*1*2*2)^3 = 64.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Charles R Greathouse IV, GP script

Crossrefs

Cf. A034710, A117720, A117723, A241846.

Programs

Magma

[n : n in [1..1000000] | (&+Intseq(n))^2 eq (&*Intseq(n))^3 ];

Mathematica

Select[Range[20000000], Plus @@ IntegerDigits[#]^2 == Times @@ IntegerDigits[#]^3 &]

PARI

for(n = 1,1000000, d = digits(n); if((sumdigits(n))^2 == prod(i = 1, #d, d[i])^3, print1(n, ", ")));

PARI

proddigits(n)=my(d=digits(n)); prod(i=1,#d,d[i])
is(n)=my(s=sumdigits(n)); if(!ispower(s,3), return(0)); s^2==proddigits(n)^3 \\ Charles R Greathouse IV, Aug 31 2015

Extensions

a(22)-a(27) from Charles R Greathouse IV, Aug 31 2015