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).

30, 105, 15015, 9699690, 37182145, 215656441, 955049953, 33426748355, 247357937827, 1448810778701, 3710369067405, 304250263527210, 102481630431415235, 1086305282573001491, 261682369333342226303, 37420578814667938361329, 241532826894674874877669

Offset: 1

Author

Michel Marcus, Jan 07 2016

Keywords

• nonn

Comments

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).

This sequence contains A159578(n) for all values of n > 1. - Altug Alkan, Jan 07 2016

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..500
• K. Alladi and P. Erdős, On an additive arithmetic function, Pacific J. Math., Volume 71, Number 2 (1977), 275-294.

Crossrefs

Cf. A046346, A097889, A159578.

Programs

PARI

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

Extensions

a(13)-a(17) from Hiroaki Yamanouchi, Jan 12 2016