cp's OEIS Frontend

A266955 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).

%I A266955 #20 Jan 15 2016 11:49:05
%S A266955 30,105,15015,9699690,37182145,215656441,955049953,33426748355,
%T A266955 247357937827,1448810778701,3710369067405,304250263527210,
%U A266955 102481630431415235,1086305282573001491,261682369333342226303,37420578814667938361329,241532826894674874877669
%N A266955 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 A266955 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 A266955 This sequence contains A159578(n) for all values of n > 1. - _Altug Alkan_, Jan 07 2016
%H A266955 Hiroaki Yamanouchi, <a href="/A266955/b266955.txt">Table of n, a(n) for n = 1..500</a>
%H A266955 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 A266955 (PARI) sopfr(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]); }
%o A266955 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 A266955 Cf. A046346, A097889, A159578.
%K A266955 nonn
%O A266955 1,1
%A A266955 _Michel Marcus_, Jan 07 2016
%E A266955 a(13)-a(17) from _Hiroaki Yamanouchi_, Jan 12 2016