A266955 - OEIS

%I #20 Jan 15 2016 11:49:05

%S 30,105,15015,9699690,37182145,215656441,955049953,33426748355,

%T 247357937827,1448810778701,3710369067405,304250263527210,

%U 102481630431415235,1086305282573001491,261682369333342226303,37420578814667938361329,241532826894674874877669

%N Intersection of A046346 (numbers that are divisible by the sum of their prime factors, counted with multiplicity) and A097889 (numbers that are products of at least two consecutive primes).

%C Alladi and Erdős ask if this sequence is infinite and give 3 terms: 2*3*5, 2*3*5*7*11*13*17*19 and 2*3*5*7*11*13*17*19*23*29*31*37*41, that is, a(1), a(4) and a(12).

%C This sequence contains A159578(n) for all values of n > 1. - _Altug Alkan_, Jan 07 2016

%H Hiroaki Yamanouchi, <a href="/A266955/b266955.txt">Table of n, a(n) for n = 1..500</a>

%H K. Alladi and P. Erdős, <a href="http://projecteuclid.org/euclid.pjm/1102811427">On an additive arithmetic function</a>, Pacific J. Math., Volume 71, Number 2 (1977), 275-294.

%o (PARI) sopfr(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]); }

%o list(lim)= {my(v=List(), p, t); for(e=2, log(lim+.5)\log(2), p=1; t=prod(i=1, e-1, prime(i)); forprime(q=prime(e), lim, t*=q/p; if(t>lim, next(2)); if (! (t % sopfr(t)), listput(v, t)); p=nextprime(p+1))); vecsort(Vec(v));} \\ adapted from A097889

%Y Cf. A046346, A097889, A159578.

%K nonn

%O 1,1

%A _Michel Marcus_, Jan 07 2016

%E a(13)-a(17) from _Hiroaki Yamanouchi_, Jan 12 2016