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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). 1
30, 105, 15015, 9699690, 37182145, 215656441, 955049953, 33426748355, 247357937827, 1448810778701, 3710369067405, 304250263527210, 102481630431415235, 1086305282573001491, 261682369333342226303, 37420578814667938361329, 241532826894674874877669 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

PROG

(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

CROSSREFS

Cf. A046346, A097889, A159578.

Sequence in context: A158445 A046301 A193873 * A205836 A043466 A044281

Adjacent sequences:  A266952 A266953 A266954 * A266956 A266957 A266958

KEYWORD

nonn

AUTHOR

Michel Marcus, Jan 07 2016

EXTENSIONS

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

STATUS

approved

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Last modified September 19 11:26 EDT 2019. Contains 327193 sequences. (Running on oeis4.)