A086538 n-th partial sum of A086537.

1, 3, 6, 12, 16, 24, 36, 49, 60, 70, 96, 112, 144, 168, 210, 240, 288, 343, 360, 396, 448, 512, 630, 648, 675, 720, 729, 768, 840, 896, 1000, 1080, 1120, 1260, 1344, 1440, 1600, 1728, 1920, 2160, 2304, 2520, 2640, 2700, 2880, 3125, 3200, 3456, 3570, 3584, 3888

Offset

1,2

Comments

Every term has a unique prime signature. Conjecture: Every prime signature occurs in the sequence.

Links

Robert Israel, Table of n, a(n) for n = 1..731

Example

a(4) = 1+2+3+6 = 12, where 1, 2, 3 and 6 are the first four terms of A086537.

Maple

ps:= proc(n) local F;
 F:= ifactors(n)[2];
 sort(F[.., 2])
end proc:
N:= 1000: # for terms before the first term > N of A086537
Cands:= [$1..N]:
R:= NULL: s:= 0: Sigs:= {}: found:= true:
for count from 1 while found do
  found:= false;
  for i from 1 to N+1-count do
    sp:= s+Cands[i];
    x:= ps(sp);
    if member(x, Sigs) then next fi;
    R:= R, sp;
    Sigs:= Sigs union {x};
    Cands:= subsop(i=NULL, Cands);
    found:= true;
    s:= sp;
    break
  od
od:
R; # Robert Israel, Jun 17 2024

Prog

(PARI) ps(n) = local(f); f = factor(n); vecsort(f[, 2]);
psUsed(v, n) = for (i = 1, n - 1, if (v == P[i], return(1))); 0;
print1(1, ", "); P = vector(70); used = vector(10000); x = 2; s = 1; for (n = 1, 70, i = x; v = ps(s + i); while (psUsed(v, n), i++; while (used[i], i++); v = ps(s + i)); used[i] = 1; P[n] = v; s += i; print1(s, ", "); while(used[x], x++)); \\ David Wasserman, Mar 15 2005

Crossrefs

Cf. A086537.

Sequence in context: A032602 A116593 A109735 * A127563 A108757 A323645

Adjacent sequences: A086535 A086536 A086537 * A086539 A086540 A086541

Keyword

nonn

Author

Amarnath Murthy, Aug 19 2003

Extensions

Corrected and extended by David Wasserman, Mar 15 2005

Status

approved