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Search: id:A138564
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| A138564 |
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a(1) = 1; a(n) = a(n-1) + (n!)^3. |
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+0
1
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| 1, 9, 225, 14049, 1742049, 374990049, 128399054049, 65676719822049, 47850402559694049, 47832576242431694049, 63649302669112063694049, 109966989623147836159694049, 241567605673714904675071694049
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By sum of cubes factorization, every a(n) > 1 is a multiple of 9, hence none of these are prime, unlike the case of sum of squares of factorials (i.e. (1!)^2 + (2!)^2+ (3!)^2+ (4!)^2 = 617 is prime; 41117342095090841723228045851817 = (1!)^2 + (2!)^2 + (3!)^2 + (4!)^2 + (5!)^2 + (6!)^2 + (7!)^2 + (8!)^2 + (9!)^2 + (10!)^2 + (11!)^2 + (12!)^2 + (13!)^2 + (14!)^2 + (15!)^2 + (16!)^2 + (17!)^2 + (18!)^2 is prime).
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FORMULA
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a(n) = SUM{k=1..n] (k!)^3 = SUM[k=1..n] A000578(A000142(n)).
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EXAMPLE
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a(18) = (1!)^3 + (2!)^3 + (3!)^3 + (4!)^3 + (5!)^3 + (6!)^3 + (7!)^3 + (8!)^3 + (9!)^3 + (10!)^3 + (11!)^3 + (12!)^3 + (13!)^3 + (14!)^3 + (15!)^3 + (16!)^3 + (17!)^3 + (18!)^3 = 262480797594664584673157017306412926841599694049.
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CROSSREFS
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Cf. A000142, A000578, A104344, A100288.
Sequence in context: A128492 A001818 A095363 this_sequence A158728 A152101 A165389
Adjacent sequences: A138561 A138562 A138563 this_sequence A138565 A138566 A138567
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 18 2008
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