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.

42, 66, 72, 78, 88, 104, 110, 130, 136, 152, 156, 160, 170, 184, 190, 200, 204, 224, 228, 230, 232, 238, 240, 248, 255, 285, 345, 435, 460, 465, 483, 525, 555, 580, 600, 609, 615, 620, 651, 696, 744, 777, 783, 812, 837, 861, 868, 888, 903, 930, 984, 987, 999

Offset: 1

Author

J. Lowell, Jan 09 2022

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A050376, A037992, A002183.

Programs

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
lista(nn) = my(vfd=list(nn), res=List()); for (n=1, nn, my(vless = select(x->(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

Extensions

More terms from Jinyuan Wang, Jan 09 2022