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 A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when 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, 2, 4, 5, 6, 2, 9, 2, 10, 4, 4, 4, 11, 2, 4, 4, 8, 2, 9, 2, 6, 6, 4, 2, 12, 3, 4, 4, 6, 2, 8, 2, 8, 4, 4, 2, 13, 2, 4, 9, 14, 2, 9, 2, 6, 4, 9, 2, 15, 2, 4, 6, 6, 2, 9, 2, 12, 4, 4, 2, 13, 4, 4, 4, 8, 2, 13, 2, 6, 4, 4, 2, 16, 2, 6, 6, 6, 2, 9, 2, 8, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of A284011. 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 Michel Marcus 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)); v305899 = rgs_transform(vector(up_to, n, A284011(n))); A305899(n) = v305899[n]; CROSSREFS Cf. A260443, A284011, A305898. Cf. also A304751. Sequence in context: A300827 A144371 A323157 * A101296 A305898 A181819 Adjacent sequences:  A305896 A305897 A305898 * A305900 A305901 A305902 KEYWORD nonn AUTHOR Antti Karttunen, Jul 01 2018 STATUS approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)