A113739 - OEIS

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A113739

Pierpont 7-almost primes. 7-almost primes of form (2^K)*(3^L)+1.

339738625, 10460353204, 83682825625, 669462604993, 2641807540225, 3761479876609, 7625597484988, 18075490334785, 35184372088833, 481469424205825, 488038239039169, 570630428688385, 1125899906842625 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	LINKS	`Eric Weisstein's World of Mathematics, Pierpont Prime` `Eric Weisstein's World of Mathematics, Almost Prime`
	FORMULA	`a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 7.`
	EXAMPLE	`a(1) = 339738625 = (2^22)(3^4)+1 = 5 5 * 5 * 17 * 29 * 37 * 149.` `a(2) = 10460353204 = (2^0)(3^21)+1 = 2 2 * 7 * 7 * 43 * 547 * 2269.` `a(3) = 83682825625 = (2^3)(3^21)+1 = 5 5 * 5 * 5 * 7 * 631 * 30313.` `a(4) = 669462604993 = (2^6)(3^21)+1 = 7 13 * 19 * 31 * 67 * 277 * 673.` `a(7) = 7625597484988 = (2^0)(3^27)+1 = 2 2 * 7 * 19 * 37 * 19441 * 19927.` `a(9) = 35184372088833 = (2^45)(3^0)+1 = 3 3 * 3 * 11 * 19 * 331 * 18837001.` `a(13) = 1125899906842625 = (2^50)(3^0)+1 = 5 5 * 5 * 41 * 101 * 8101 * 268501.` `a(16) = 5559060566555524 = (2^0)(3^33)+1 = 2 2 * 7 * 67 * 661 * 25411 * 176419.` `a(28) = 9223372036854775809 = (2^63)(3^0)+1 = 3 3 * 3 * 19 * 43 * 5419 * 77158673929.`
	CROSSREFS	`Intersection of A046308 and A055600.` `A005109 gives the Pierpont primes, which are primes of the form (2^K)(3^L)+1.` `A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)(3^L)+1.` `A112797 gives the Pierpont 3-almost primes, of the form (2^K)(3^L)+1.` `A111344 gives the Pierpont 4-almost primes, of the form (2^K)(3^L)+1.` `A111345 gives the Pierpont 5-almost primes, of the form (2^K)(3^L)+1.` `A111346 gives the Pierpont 6-almost primes, of the form (2^K)(3^L)+1.` `A113740 gives the Pierpont 8-almost primes, of the form (2^K)(3^L)+1.` `A113741 gives the Pierpont 9-almost primes, of the form (2^K)(3^L)+1.` `Sequence in context: A035794 A022239 A204337 * A159448 A015381 A186628` `Adjacent sequences: A113736 A113737 A113738 * A113740 A113741 A113742`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 08 2005`
	EXTENSIONS	`Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 08 2005`

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Last modified February 15 04:23 EST 2012. Contains 205694 sequences.