A130688 Numbers n with following property: suppose n^6 = d1 d2 d3 ...dk in decimal; then d1! + d2! + ... + dk! is a square.
1, 6, 747, 2802, 10000, 10256, 11876, 13875, 14623, 14710, 17117, 18090, 23919, 26569, 34282, 35402, 40515, 41202, 41850, 42195, 44684, 48396, 54698, 58509, 59293, 59644, 59900, 65502, 67795, 74004, 75320, 79593, 82677, 82713, 83402
Offset: 1
Examples
a(2) = 6, because 6^6 = 46656, and (4!+6!+6!+5!+6!)^(1/2) = 48 is an integer.
Programs
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Maple
A061602 := proc(n) local digs ; digs := convert(n,base,10) ; add(factorial(op(i,digs)),i=1..nops(digs)) ; end: isA130687 := proc(n) RETURN(issqr(A061602(n))) ; end: isA130688 := proc(n) RETURN(isA130687(n^6)) ; end: for n from 1 to 130000 do if isA130688(n) then printf("%d, ",n) ; fi : od:
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PARI
for(n=1,10^5,m=n^6;s=0;while(m,s+=(m%10)!;m\=10);if(issquare(s),print1(n",")))
Extensions
Edited by R. J. Mathar and Martin Fuller, Jul 13 2007
Comments