A065770 - OEIS

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A065770

Number of prime cascades to reach 1, where a prime cascade (A065769) is multiplicative with a(p(m)^k)=p(m-1)*p(m)^(k-1).

0, 1, 2, 2, 3, 2, 4, 3, 3, 3, 5, 3, 6, 4, 3, 4, 7, 3, 8, 3, 4, 5, 9, 4, 4, 6, 4, 4, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 4, 13, 4, 14, 5, 4, 9, 15, 5, 5, 4, 7, 6, 16, 4, 5, 4, 8, 10, 17, 4, 18, 11, 4, 6, 6, 5, 19, 7, 9, 4, 20, 5, 21, 12, 4, 8, 5, 6, 22, 5, 5, 13, 23, 4, 7, 14, 10, 5, 24, 4, 6, 9, 11 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	FORMULA	`Inverse of primes, powers of 2 and primorials in sense that a(A000040(n))=n; a(A000079(n))=n; a(A002110(n))=n. If n>0: a(3^n)=n+1; a(2^n*3^k)=n+k; a(p(k)^n)=n+k-1; a(n!)=A022559(n).`
	EXAMPLE	`a(50)=4 since the cascade goes from 50=2^15^2 to 15=3^15^1 to 6=2^1*3^1 to 2=2^1 to 1.`
	CROSSREFS	`Sequence in context: A087050 A163870 A155043 * A086375 A107324 A023522` `Adjacent sequences: A065767 A065768 A065769 * A065771 A065772 A065773`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Nov 19 2001`

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Last modified February 17 16:00 EST 2012. Contains 206050 sequences.