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 A325045 Number of factorizations of n whose conjugate as an integer partition has no ones. 4
 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS After a(1) = 1, a(n) is the number of factorizations of n with at least two factors, the largest two of which are equal. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE The initial terms count the following factorizations: 1: {} 4: 2*2 8: 2*2*2 9: 3*3 16: 2*2*2*2 16: 4*4 18: 2*3*3 25: 5*5 27: 3*3*3 32: 2*2*2*2*2 32: 2*4*4 36: 2*2*3*3 36: 6*6 48: 3*4*4 49: 7*7 50: 2*5*5 54: 2*3*3*3 64: 2*2*2*2*2*2 64: 2*2*4*4 64: 4*4*4 64: 8*8 MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]]; Table[Length[Select[facs[n], FreeQ[conj[#], 1]&]], {n, 1, 100}] PROG (PARI) A325045(n, m=n, facs=List([])) = if(1==n, (0==#facs || (#facs>=2 && facs[1]==facs[2])), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A325045(n/d, d, newfacs))); (s)); \\ Antti Karttunen, May 03 2022 CROSSREFS Cf. A001055, A001222, A002865, A096276, A114324, A122111, A318950, A319005, A319916, A320322, A321648, A325039, A353645 [= a(n^2)]. Sequence in context: A307832 A037047 A118917 * A204293 A206479 A219484 Adjacent sequences: A325042 A325043 A325044 * A325046 A325047 A325048 KEYWORD nonn AUTHOR Gus Wiseman, Mar 27 2019 EXTENSIONS More terms from Antti Karttunen, May 03 2022 STATUS approved

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Last modified December 11 05:29 EST 2023. Contains 367717 sequences. (Running on oeis4.)