A159578 Dividend associated with A116536.

2, 30, 9699690, 304250263527210, 267064515689275851355624017992790, 5766152219975951659023630035336134306565384015606066319856068810, 962947420735983927056946215901134429196419130606213075415963491270, 29819592777931214269172453467810429868925511217482600306406141434158090

Offset

1,1

Comments

a(2)-a(4) are mentioned by Alladi and Erdős (1977). They conjectured that this sequence is infinite. - Amiram Eldar, Nov 02 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..80

Krishnaswami Alladi and Paul Erdős, On an additive arithmetic function, Pacific Journal of Mathematics, Vol. 71, No. 2 (1977), pp. 275-294, alternative link. See p. 290.

Formula

a(n) = A002110(A051838(n)). - Amiram Eldar, Nov 02 2020

Example

a(2) = 30 because 2*3*5 = 30, 2+3+5 = 10, and 30/10 = 3 in A116536.

Maple

# First define t1, the sequence A051838.
t1:=[1, 3, 8, 13, 23, 38, 39, 41, 43, 48, 50, 53, 56, 57, 58, 66, 68,
70, 73, 77, 84, 90, 94, 98, 126, 128, 134, 140, 143, 145, 149,
151, 153, 157, 160, 164, 167, 168, 172, 174, 176, 182, 191,
194, 196, 200, 210, 212, 215, 217, 218, 219, 222, 225, 228,
229];
p:=ithprime;
num:=n->mul(p(i), i=1..t1[n]);
s:=[num(i), i=1..11)];

Mathematica

seq = {}; sum = 0; prod = 1; p = 1; Do[p = NextPrime[p]; prod *= p; sum += p; If[Divisible[prod, sum], AppendTo[seq, prod]], {50}]; seq (* Amiram Eldar, Nov 02 2020 *)
Module[{nn=50, s, p}, s=Accumulate[Prime[Range[nn]]]; p=FoldList[Times, Prime[Range[ nn]]]; Select[Thread[{p, s}], Divisible[#[[1]], #[[2]]]&]][[All, 1]] (* Harvey P. Dale, Jun 07 2022 *)

Crossrefs

Intersection of A002110 and A036844.

Cf. A051838, A116536.

Sequence in context: A292048 A062008 A091776 * A221192 A178194 A069460

Adjacent sequences: A159575 A159576 A159577 * A159579 A159580 A159581

Keyword

easy,nonn

Author

Enoch Haga, Apr 16 2009

Extensions

Corrected by N. J. A. Sloane, Oct 02 2011 (all the terms were wrong).

Status

approved