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 A261778 Positive numbers n such that (digitsum(n))^2 equals (product of digits(n))^3. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence is infinite because it contains all the numbers made of k fours and 8^k-4k ones. - Giovanni Resta, Sep 01 2015 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Charles R Greathouse IV, GP script EXAMPLE 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. MATHEMATICA Select[Range[20000000], Plus @@ IntegerDigits[#]^2 == Times @@ IntegerDigits[#]^3 &] PROG (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 (Magma) [n : n in [1..1000000] | (&+Intseq(n))^2 eq (&*Intseq(n))^3 ]; CROSSREFS Cf. A034710, A117720, A117723, A241846. Sequence in context: A154807 A076164 A234661 * A268278 A073038 A107650 Adjacent sequences: A261775 A261776 A261777 * A261779 A261780 A261781 KEYWORD nonn,base AUTHOR K. D. Bajpai, Aug 31 2015 EXTENSIONS a(22)-a(27) from Charles R Greathouse IV, Aug 31 2015 STATUS approved

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Last modified July 23 06:44 EDT 2024. Contains 374544 sequences. (Running on oeis4.)