1,4

Quetian Superfactorization proceeds by factoring a natural number to its unique prime-exponent factorization (p1^e1 * p2^e2 * ... pj^ej) and then factoring recursively each of the (nonzero) exponents in similar manner, until unity-exponents are finally encountered.

A. Karttunen, Scheme-program for computing this sequence.

Additive with a(p^e) = 1 + a(e).

a(64) = 3, as 64 = 2^6 = 2^(2^1*3^1) and there are three non-1 nodes in that superfactorization. Similarly, for 360 = 2^(3^1) * 3^(2^1) * 5^1 we get a(360) = 5. a(65536) = a(2^(2^(2^(2^1)))) = 4.

a(n) = A106493(A106444(n)). a(n) = A106491(n)-A064372(n). Cf. also A106492. After n=1 differs from A038548 for the first time at n=24, where A038548(24)=4, while a(24)=3.

Adjacent sequences: A106487 A106488 A106489 this_sequence A106491 A106492 A106493

Sequence in context: A128428 A056171 A076755 this_sequence A122375 A038548 A068108

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com) May 09 2005 based on Leroy Quet's (qq-quet(AT)mindspring.com) message ('Super-Factoring' An Integer) posted to SeqFan-mailing list on Dec 06 2003.