The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A106491

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A106491

Total number of bases and exponents in Quetian Superfactorization of n, including the unity-exponents at the tips of branches.
(history; published version)

#28 by Charles R Greathouse IV at Fri Jun 02 22:24:01 EDT 2017

STATUS

editing

approved

#27 by Charles R Greathouse IV at Fri Jun 02 22:23:58 EDT 2017

PROG

A028234(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); } \/* after Michel Marcus *\/

STATUS

approved

editing

#26 by N. J. A. Sloane at Thu Mar 23 11:42:29 EDT 2017

STATUS

proposed

approved

#25 by Indranil Ghosh at Thu Mar 23 11:35:18 EDT 2017

STATUS

editing

proposed

#24 by Indranil Ghosh at Thu Mar 23 11:34:38 EDT 2017

PROG

(PARI)

A067029(n) = if(n<2, 0, factor(n)[1, 2]);

A028234(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); } \* after Michel Marcus *\

a(n) = if(n<2, 1, if(A028234(n)==1, 1 + a(A067029(n)), 1 + a(A067029(n)) + a(A028234(n))));

for(n=1, 150, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017, after formula by Antti Karttunen

STATUS

proposed

editing

#23 by Antti Karttunen at Thu Mar 23 11:14:48 EDT 2017

STATUS

editing

proposed

#22 by Antti Karttunen at Thu Mar 23 11:10:12 EDT 2017

FORMULA

From Antti Karttunen, Mar 23 2017: (Start)

a(1) = 1, and for n > 1, if A028234(n) = 1, a(n) = 1 + a(A067029(n)), otherwise a(n) = 1 + a(A067029(n)) + a(A028234(n)).

If n is a prime power p^k (a term of A000961), a(n) = 1 + a(k).

(End)

a(n) = A106490(n) + A064372(n).

CROSSREFS

Cf. A000961, A028234, A064372, A067029, A106444, A106490, A106492, A106494.

#21 by Antti Karttunen at Thu Mar 23 11:03:54 EDT 2017

FORMULA

Other identities. For all n >= 1:

a(n) = A106490(n)+A064372(n).

a(n) = A106494(A106444(n)).

CROSSREFS

a(n) = A106494(A106444(n)). a(n) = A106490(n)+A064372(n). Cf. also A106492.

Cf. A064372, A106444, A106490, A106492, A106494.

#20 by Antti Karttunen at Thu Mar 23 11:00:47 EDT 2017

PROG

(Scheme, with memoization-macro definec)

(definec (A106491 n) (cond ((= 1 n) n) ((= 1 (A028234 n)) (+ 1 (A106491 (A067029 n)))) (else (+ 1 (A106491 (A067029 n)) (A106491 (A028234 n)))))) ;; Antti Karttunen, Mar 23 2017

#19 by Antti Karttunen at Thu Mar 23 05:25:35 EDT 2017

LINKS

<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

STATUS

approved

editing