cp's OEIS Frontend

A350641 Numbers k such that the product of k and all terms < k in A050376 has more divisors than the product of all terms < k in A050376 and the smallest term > k in A050376.

%I A350641 #21 Jan 27 2022 21:12:37
%S A350641 42,66,72,78,88,104,110,130,136,152,156,160,170,184,190,200,204,224,
%T A350641 228,230,232,238,240,248,255,285,345,435,460,465,483,525,555,580,600,
%U A350641 609,615,620,651,696,744,777,783,812,837,861,868,888,903,930,984,987,999
%N A350641 Numbers k such that the product of k and all terms < k in A050376 has more divisors than the product of all terms < k in A050376 and the smallest term > k in A050376.
%C A350641 Multiplying a number in this sequence by all numbers in A050376 less than it will give a number less than, but with more divisors than, a number in A037992 with comparable magnitude.
%e A350641 The product of 42 and all terms < 42 in A050376 has 276480 divisors. The product of all terms < 42 in A050376 and the smallest term > 42 (i.e., 43) in A050376 has only 262144 divisors. Thus, 42 is a term of this sequence.
%o A350641 (PARI) list(lim) = my(v=primes(primepi(lim)), t); forprime(p=2, sqrt(lim), t=p; while((t=t^2)<=lim, v=concat(v, t))); vecsort(v); \\ A050376
%o A350641 lista(nn) = my(vfd=list(nn), res=List()); for (n=1, nn, my(vless = select(x->(x<n), vfd)); if (#vless, my(vmore = select(x->(x>n), vfd)); if (#vmore, my(p = vecprod(vless)); if (numdiv(p*n) > numdiv(p*vmore[1]), listput(res, n));););); res; \\ _Michel Marcus_, Jan 10 2022
%Y A350641 Cf. A050376, A037992, A002183.
%K A350641 nonn
%O A350641 1,1
%A A350641 _J. Lowell_, Jan 09 2022
%E A350641 More terms from _Jinyuan Wang_, Jan 09 2022