A086492 Group the natural numbers such that the n-th group sum is divisible by prime(n): (1, 2, 3), (4, 5), (6, 7, 8, 9), (10, 11), (12, 13, 14, 15, 16, 17, 18, 19, 20, 21), ... Sequence contains (the sum of the terms in the n-th group)/prime(n): a(n) = A086491(n)/prime(n).

3, 3, 6, 3, 15, 18, 14, 2, 30, 18, 75, 111, 98, 116, 12, 180, 12, 52, 140, 306, 115, 185, 15, 285, 115, 85, 15, 185, 506, 390, 618, 494, 13, 156, 689, 497, 91, 497, 1140, 888, 1394, 459, 1161, 950, 1730, 693, 1953, 693, 189, 252, 630, 693, 2387, 33, 1419, 33, 1419

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Example

a(4) = 3 = A086491(4)/prime(4) = 21/7.

Mathematica

k = 0; Table[p = Prime[n]; k++; sm = 0; While[sm = sm + k; Mod[sm, p] > 0, k++]; sm/p, {n, 50}] (* T. D. Noe, Mar 19 2014 *)

Prog

(Python)
from itertools import count
from sympy import prime, primerange
def aupton(terms):
    alst, naturals = [], count(1)
    for p in primerange(1, prime(terms)+1):
        s = next(naturals)
        while s%p: s += next(naturals)
        alst.append(s//p)
    return alst
print(aupton(57)) # Michael S. Branicky, Jun 09 2021

Crossrefs

Cf. A086491, A086493.

Sequence in context: A120909 A086222 A278663 * A372036 A143305 A051472

Adjacent sequences: A086489 A086490 A086491 * A086493 A086494 A086495

Keyword

nonn

Author

Amarnath Murthy, Jul 28 2003

Extensions

More terms from Ray Chandler, Sep 16 2003

Status

approved