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A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z. 2
1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 4, 4, 2, 8, 9, 4, 5, 6, 2, 10, 2, 11, 4, 4, 4, 12, 2, 4, 4, 8, 2, 10, 2, 6, 6, 4, 2, 13, 3, 14, 4, 6, 2, 8, 15, 8, 4, 4, 2, 16, 2, 4, 17, 18, 15, 10, 2, 6, 4, 10, 2, 19, 2, 4, 6, 6, 15, 10, 2, 13, 20, 4, 2, 16, 4, 4, 4, 8, 2, 16, 15, 6, 4, 4, 15, 21, 2, 6, 6, 22, 2, 10, 2, 8, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Restricted growth sequence transform of ordered pair [A046523(n), A284011(n)].

For all i, j: a(i) = a(j) => A305892(i) = A305892(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; };

pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };

A284010(n) = { if(!bitand(n, (n-1)), 0, my(p=0, f=vecsort(factor(pfps(n))[, 2], , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i])); }

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

A284011(n) = A284010(A260443(n));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

Aux305898(n) = [A046523(n), A284011(n)];

v305898 = rgs_transform(vector(up_to, n, Aux305898(n)));

A305898(n) = v305898[n];

CROSSREFS

Cf. A046523, A284011, A305892, A305899.

Cf. also A305790.

Sequence in context: A323157 A305899 A101296 * A181819 A302046 A077462

Adjacent sequences:  A305895 A305896 A305897 * A305899 A305900 A305901

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 01 2018

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)