A159578 Dividend associated with A116536.

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

Offset: 1

Author

Enoch Haga, Apr 16 2009

Keywords

• easy
• nonn

Comments

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

Examples

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

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.

Crossrefs

Intersection of A002110 and A036844.

Cf. A051838, A116536.

Programs

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 *)

Formula

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

Extensions

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