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 A305896 Filter sequence combining prime signature of n (A046523) and the cardinality of invphi (A014197). 3
 1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 10, 11, 3, 12, 3, 13, 10, 8, 3, 14, 7, 10, 15, 16, 3, 17, 3, 18, 10, 10, 10, 19, 3, 10, 10, 20, 3, 21, 3, 22, 23, 8, 3, 24, 7, 23, 10, 16, 3, 25, 10, 26, 10, 8, 3, 27, 3, 10, 23, 28, 10, 17, 3, 23, 10, 17, 3, 29, 3, 10, 23, 23, 10, 17, 3, 30, 31, 8, 3, 32, 10, 10, 10, 33, 3, 34, 10, 22, 10, 10, 10, 35, 3, 23, 23, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of ordered pair [A046523(n), A014197(n)]. For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A097946(i) = A097946(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 PROG (PARI) up_to = 65537; rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; }; A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ This function from M. F. Hasler, Oct 05 2009 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523 Aux305896(n) = [A046523(n), A014197(n)]; v305896 = rgs_transform(vector(up_to, n, Aux305896(n))); A305896(n) = v305896[n]; CROSSREFS Cf. A014197, A046523, A305801. Cf. also A097946. Sequence in context: A322810 A322024 A326203 * A322588 A323401 A326199 Adjacent sequences:  A305893 A305894 A305895 * A305897 A305898 A305899 KEYWORD nonn AUTHOR Antti Karttunen, Jul 01 2018 STATUS approved

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Last modified October 16 06:10 EDT 2019. Contains 328046 sequences. (Running on oeis4.)