A269525 a(1) = 1, a(n) is the sum of m < n for which a(m) has at most as many divisors as n.

1, 1, 3, 6, 6, 15, 6, 28, 6, 37, 16, 66, 16, 47, 61, 100, 45, 125, 45, 162, 94, 115, 45, 240, 45, 137, 163, 306, 98, 347, 128, 365, 252, 252, 252, 456, 128, 252, 252, 477, 128, 558, 128, 437, 481, 341, 128, 819, 128, 572, 387, 623, 128, 988

Offset

1,3

Links

Peter Kagey, Table of n, a(n) for n = 1..1000

Example

a(1) = 1;
a(2) = 1 because a(1) has at most as many divisors as 2;
a(3) = 3 because a(1) and a(2) have at most as many divisors as 3;
a(4) = 6 because a(1), a(2), and a(3) have at most as many divisors as 4;
a(5) = 6 because a(1), a(2), and a(3) have at most as many divisors as 5.

Mathematica

a = {1}; Do[d = DivisorSigma[0, n]; AppendTo[a, Total@ Select[Range[n - 1], DivisorSigma[0, a[[#]]] <= d &]], {n, 2, 54}]; a (* Michael De Vlieger, Mar 24 2016 *)

Prog

(Java)
int[] terms = new int[100];
terms[0] = 1;
for (int i = 1; i < 100; i++) {
    int count = 0;
    for (int j = 0; j < i; j++) {
        if (divisors(terms[j]) <= divisors(i+1)) {
            count = count + j + 1;
        }
    }
    terms[i] = count;
}
(PARI) lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); for (n=2, nn, va[n] = sum(k=1, n-1, k*(numdiv(va[k]) <= numdiv(n))); print1(va[n], ", "); ); } \\ Michel Marcus, Feb 29 2016

Crossrefs

Sequence in context: A119306 A107972 A238775 * A341885 A390806 A364372

Adjacent sequences: A269522 A269523 A269524 * A269526 A269527 A269528

Keyword

easy,nonn

Author

Alec Jones, Feb 29 2016

Status

approved