OFFSET
1,2
COMMENTS
EXAMPLE
Row n=4 of A036035 contains 16=2^4, 24=2^3*3, 36=2^2*3^2, 60=2^2*3*5 and 210=2*3*5*7. The 16 has k=1 distinct prime factor; 24 and 36 have k=2 distinct prime factors; 60 has k=3 distinct prime factors; 210 has k=4 distinct prime factors (see A001221).
T(4,1)=A001055(16)=5.
T(4,3)=A001055(60)=11.
T(4,4)=A001055(210)=15.
Table starts
1;
2, 2;
3, 4, 5;
5, 16, 11, 15;
7, 28, 47, 36, 52;
11, 79, 156, 166, 135, 203;
15, 134, 408, 588, 667, 566, 877;
22, 328, 1057, 2358, 2517, 2978, 2610, 4140;
30, 536, 3036, 6181, 10726, 11913, 14548, 13082, 21147;
42, 1197, 6826, 21336, 40130, 53690, 61421, 76908, 70631, 115975;
...
MAPLE
A036035 := proc(n) local pr, L, a ; a := [] ; pr := combinat[partition](n) ; for L in pr do mul(ithprime(i)^op(-i, L), i=1..nops(L)) ; a := [op(a), %] ; od ; RETURN(a) ; end: A001221 := proc(n) local ifacts ; ifacts := ifactors(n)[2] ; nops(ifacts) ; end: listProdRep := proc(n, mincomp) local dvs, resul, f, i, rli ; resul := 0 ; if n = 1 then RETURN(1) elif n >= mincomp then dvs := numtheory[divisors](n) ; for i from 1 to nops(dvs) do f := op(i, dvs) ; if f =n and f >= mincomp then resul := resul+1 ; elif f >= mincomp then rli := listProdRep(n/f, f) ; resul := resul+rli ; fi ; od ; fi ; RETURN(resul) ; end: A001055 := proc(n) listProdRep(n, 2) ; end: A093936 := proc(n, k) local a, a036035, j ; a := 0 ; a036035 := A036035(n) ; for j in a036035 do if A001221(j) = k then a := a+A001055(j) ; fi ; od ; RETURN(a) ; end: for n from 1 to 10 do for k from 1 to n do printf("%d, ", A093936(n, k)) ; od : od : # R. J. Mathar, Jul 27 2007
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alford Arnold, May 23 2004
EXTENSIONS
More terms from Alford Arnold, Nov 19 2005
More terms from R. J. Mathar, Jul 27 2007
STATUS
approved