id:A141702 - OEIS Search Results

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a(n) = number of Carmichael numbers of the form prime(n)*prime(n')*prime(n") with n > n' > n".

+0
5

0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 1 (list; graph; listen)

	OFFSET	`1,7`
	COMMENT	`The formula and PARI code uses Korselt's criterion. This sequence is a somewhat trivial variant of the more interesting sequence giving the number of Carmichael numbers of the form prime(n)prime(n')prime(n") with n < n' < n" (known to be finite for given n).`
	FORMULA	`a(n) = # { pqr \| p=prime(n) > q=prime(n') > r=prime(n") ; p-1 \| pqr-1 ; q-1 \| pqr-1 ; r-1 \| pqr-1 }`
	EXAMPLE	`a(7)=2 is the first nonzero term since 561 = 31117 and 1105 = 51317 are the two smallest Carmichael numbers and there's no other Carmichael number having prime(7)=17 as largest factor.`
	PROGRAM	`(PARI) A141702(n) = { local( p=prime(n), c=0 ); forprime( q=5, p-2, forprime( r=3, q-2, (pqr-1)%(p-1)==0 && (pqr-1)%(q-1)==0 && (pqr-1)%(r-1)==0 && c++ )); c }`
	CROSSREFS	`Cf. A002997 and references therein ; A087788 ; A141703 ff.` `Sequence in context: A083905 A045706 A045634 this_sequence A113313 A099200 A093578` `Adjacent sequences: A141699 A141700 A141701 this_sequence A141703 A141704 A141705`
	KEYWORD	`easy,nonn`
	AUTHOR	`M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 30 2008`

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Last modified December 7 08:40 EST 2009. Contains 170430 sequences.

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