A111096 - OEIS

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A111096

Partial sums of A137701.

16, 232, 59281, 10059281, 4049575228945, 1950244643588320, 30041944445326335483061, 32095019157463691981298869, 142108579247039194637916834814494 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`a(n) is prime for n = 3, 4, ..., a(n) is semiprime for n = 7, 8, 11, ...`
	FORMULA	`a(n) = sum[i = 1 to n]A001358(i)^A000040(i).`
	EXAMPLE	`a(1) = 16 because semiprime(1)^prime(1) = 4^2 = 16.` `a(2) = 232 because 4^2 + 6^3 = 232.` `a(3) = 59281 = 4^2 + 6^3 + 9^5, which is a prime.` `a(4) = 10059281 = 4^2 + 6^3 + 9^5 + 10^7, which is a prime.` `a(7) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 = 428081461 * 70178102025601, which is semiprime.` `a(8) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 + 22^19 = 47 * 682872748031142382580827, which is semiprime.` `a(11) = 4^2 + 6^3 + 9^5 + 10^7 + 14^11 + 15^13 + 21^17 + 22^19 + 25^23 + 26^29 + 33^31 = 17 * 6974026787528502313510746401919931843721072911 which is semiprime.`
	CROSSREFS	`Cf. A000040, A001358, A137701, A125580.` `Sequence in context: A028340 A166903 A119463 * A161591 A103975 A162791` `Adjacent sequences: A111093 A111094 A111095 * A111097 A111098 A111099`
	KEYWORD	`easy,nonn,less`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 13 2005`

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Last modified February 16 01:29 EST 2012. Contains 205860 sequences.