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 A237290 Sum of positive numbers k <= sigma(n) that are a sum of any subset of distinct divisors of n. 3
 1, 6, 8, 28, 12, 78, 16, 120, 52, 144, 24, 406, 28, 192, 192, 496, 36, 780, 40, 903, 256, 288, 48, 1830, 124, 336, 320, 1596, 60, 2628, 64, 2016, 384, 432, 384, 4186, 76, 480, 448, 4095, 84, 4656, 88, 2688, 2184, 576, 96, 7750, 228, 2976, 576, 3136, 108, 7260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 FORMULA a(n) = A184387(n) - A237289(n). a(p) = 2(p+2) for odd primes p. a(n) = A184387(n) for practical numbers n (A005153), a(n) < A184387(n) for numbers n that are not practical (A237287). EXAMPLE For n = 5, a(5) = 1 + 5 + 6 = 12 (each of the numbers 1, 5 and 6 is the sum of a subset of distinct divisors of 5). The numbers n = 14 and 15 is an interesting pair of consecutive numbers with identical value of sigma(n) such that simultaneously a(14) = a(15) and A237289(14) = A237289(15). a(14) = 1+2+3+7+8+9+10+14+15+16+17+21+22+23+24 = a(15) = 1+3+4+5+6+8+9+15+16+18+19+20+21+23+24 = 192. MAPLE isSumDist := proc(n, k) local dvs, s ; dvs := numtheory[divisors](n) ; for s in combinat[powerset](dvs) do add(m, m=op(s)) ; if % = k then return true; end if; end do: false ; end proc: A237290 := proc(n) local a; a := 0 ; for k from 1 to numtheory[sigma](n) do if isSumDist(n, k) then a := a+k; end if; end do: end proc: seq(A237290(n), n=1..20) ; # R. J. Mathar, Mar 13 2014 MATHEMATICA a[n_] := Plus @@ Union[Plus @@@ Subsets@ Divisors@ n]; Array[a, 54] (* Giovanni Resta, Mar 13 2014 *) PROG (PARI) padbin(n, len) = {b = binary(n); while(length(b) < len, b = concat(0, b); ); b; } a(n) = {vks = []; d = divisors(n); nbd = #d; for (i=1, 2^nbd-1, b = padbin(i, nbd); onek = sum(j=1, nbd, d[j]*b[j]); vks = Set(concat(vks, onek)); ); sum(i=1, #vks, vks[i]); } \\ Michel Marcus, Mar 09 2014 (Python) from sympy import divisors def A237290(n): ds = divisors(n) c, s = {0}, sum(ds) for d in ds: c |= {a+d for a in c} return sum(a for a in c if 1<=a<=s) # Chai Wah Wu, Jul 05 2023 CROSSREFS Cf. A119348, A005153, A184387, A237287, A237289. Sequence in context: A024873 A066231 A267477 * A229335 A007829 A345003 Adjacent sequences: A237287 A237288 A237289 * A237291 A237292 A237293 KEYWORD nonn AUTHOR Jaroslav Krizek, Mar 02 2014 STATUS approved

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Last modified October 4 02:45 EDT 2023. Contains 365872 sequences. (Running on oeis4.)