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

1,2

Comments

Numbers n such that n^6 is in A130687.

Links

Table of n, a(n) for n=1..35.

Example

a(2) = 6, because 6^6 = 46656, and (4!+6!+6!+5!+6!)^(1/2) = 48 is an integer.

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:

Prog

(PARI) for(n=1, 10^5, m=n^6; s=0; while(m, s+=(m%10)!; m\=10); if(issquare(s), print1(n", ")))

Crossrefs

Cf. A130687, A089185, A126076, A126077, A126078.

Sequence in context: A289365 A251810 A283787 * A214009 A332176 A088217

Adjacent sequences: A130685 A130686 A130687 * A130689 A130690 A130691

Keyword

nonn,base

Author

Yalcin Aktar, Jun 30 2007

Extensions

Edited by R. J. Mathar and Martin Fuller, Jul 13 2007

Status

approved