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 A035796 Words over signatures (derived from multisets and multinomials). 3
 1, 1, 2, 2, 3, 18, 4, 48, 6, 5, 36, 100, 144, 6, 200, 180, 600, 7, 450, 900, 294, 24, 300, 1800, 8, 882, 7200, 448, 1200, 1470, 4410, 9, 1568, 22050, 648, 7200, 3136, 1800, 9408, 10, 14700, 2592, 16200, 1960, 56448, 900, 29400, 6048, 22050, 18144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A reordering of A049009(n)=A049009(p(n)): distribution of words by numeric partition where the partition sequence: p(n)=[1],[2],[1,1],[3],[2,1],[1,1,1],[4],[3,1],[2,2],[2,1,1],... (A036036) is encoded by prime factorization ([P1,P2,P3,...] with P1 >= P2 >= P3 >= ... is encoded as 2^P1 * 3^P2 * 5^P3 *...): ep(n)=2,4,6,8,12,30,16,24,36,60, ... (A036035(n)) and then sorted: s(m)=2,4,6,8,12,16,24,30,32,36,48,60,... (A025487(m)). Hence A035796(n) = A049009(s(m)). REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..10000 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. FORMULA a(n) = A049009(p) where p is such that A036035(p) = A025487(n). [Corrected by Andrew Howroyd and Sean A. Irvine, Oct 18 2020] EXAMPLE 27 = a(5) + a(6) + a(9) since a8(4) = 3, a12(5) = 18, a30(8) = 6; 256 = a(7) + a(8) + a(11) + a(13) + a(22) = 4 + 48 + 36 + 144 + 24 27 = a(5) + a(6) + a(9) = A049009(4) + A049009(5) + A049009(6) = 3 + 18 + 6 since A036035(4) = 8 = A025487(4+1), A036035(5) = 12 = A025487(5+1), A036035(6) = 30 = A025487(8+1);... PROG (PARI) \\ here P is A025487 as vector and C is A049009 by partition. GenS(lim)={my(L=List(), S=[1]); forprime(p=2, oo, listput(L, S); my(pp=vector(logint(lim, p), i, p^i)); S=concat([k*pp[1..min(if(k>1, my(f=factor(k)[, 2]); f[#f], oo), logint(lim\k, p))] | k<-S]); if(!#S, return(Set(concat(L)))) )} P(n)={my(lim=1, v=[1]); while(#vt==S[k], sig))!) * prod(k=1, #sig, sig[k]!))} seq(n)={[C(factor(t)[, 2]) | t<-P(n)]} \\ Andrew Howroyd, Oct 18 2020 CROSSREFS Cf. A000312, A025487, A019575, A001700, A005651, A036035, A036036, A025487, A049009. Sequence in context: A164022 A089751 A137909 * A049009 A101817 A058159 Adjacent sequences: A035793 A035794 A035795 * A035797 A035798 A035799 KEYWORD nonn AUTHOR Alford Arnold EXTENSIONS More terms and additional comments from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 02 2001 a(1)=1 inserted by Andrew Howroyd and Sean A. Irvine, Oct 18 2020 STATUS approved

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Last modified September 17 04:45 EDT 2024. Contains 375985 sequences. (Running on oeis4.)