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Search: id:A076804
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| A076804 |
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a(n) = least positive integer k satisfying Omega(k) = Omega(k+1)+Omega(k+2)....+Omega(k+n), where Omega = A001222 = number of prime factors, counting multiplicity. |
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1
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| 2, 12, 64, 4608, 2304, 193536, 1572864, 566231040, 1879048192, 167503724544, 850403524608, 79164837199872, 3595815339687936, 69084514596421632, 1801439850948198400
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(16) > 2^63. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 27 2008]
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EXAMPLE
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k=2 is the least solution of Omega(k) = Omega(k+1), so a(1) = 2.
k=12 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2), so a(2) = 12.
k=64 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2)+Omega(k+3), so a(3) = 64.
k=4608 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2)+Omega(k+3)+Omega(k+4), so a(4) = 4608.
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PROGRAM
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(PARI) A078114(n, ok=0)={ local( MIN=n+sum(i=2, n, bigomega(i)), t, k ); until( !t & k==ok+n, while( MIN>t=bigomega(ok++), ); k=ok; while( 0 < t-=bigomega(k++), )); ok} (M. F. Hasler, Jun 17 2007)
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CROSSREFS
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Cf. A076183, A001222.
Sequence in context: A025599 A126737 A097632 this_sequence A039633 A020062 A000954
Adjacent sequences: A076801 A076802 A076803 this_sequence A076805 A076806 A076807
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KEYWORD
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hard,more,nonn
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AUTHOR
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Shyam Sunder Gupta (guptass(AT)rediffmail.com), Nov 17 2002
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EXTENSIONS
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Corrected & edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 17 2007
a(9)-a(15) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 27 2008
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