A342012 Primorial deflation of the n-th colossally abundant number: the unique integer k such that A108951(k) = A004490(n).

2, 3, 6, 10, 20, 30, 42, 84, 132, 156, 312, 468, 780, 1020, 1140, 1380, 2760, 3480, 3720, 5208, 7812, 9324, 10332, 10836, 21672, 23688, 26712, 29736, 49560, 51240, 56280, 59640, 61320, 96360, 104280, 208560, 219120, 328680, 352440, 384120, 453960, 472680, 482040, 500760, 510120, 528840, 594360, 613080, 641160, 650520, 1301040

Offset: 1

Author

Antti Karttunen, Mar 08 2021

Keywords

• nonn

Comments

In contrast to A329902, this sequence is monotonic, because each term is obtained from the previous, either by multiplying it by 2, or by "bumping" one [or hypothetically: two] of its prime factors one step up (i.e., replacing it with the next larger prime), and both operations are guaranteed to make the number larger.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004490, A005940, A073751, A108951, A319626, A329900, A342010 [= A001222(a(n))], A342011, A342013.

Cf. also A217867, A329902.

Programs

PARI

v073751 = readvec("b073751_to.txt");
A073751(n) = v073751[n];
A004490list(v073751) = { my(v=vector(#v073751)); v[1] = 2; for(n=2,#v,v[n] = v073751[n]*v[n-1]); (v); };
v004490 = A004490list(v073751);
A004490(n) = v004490[n];
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A319626(n) = (n / gcd(n, A064989(n)));
A342012(n) = A319626(A004490(n));

Formula

a(n) = A319626(A004490(n)) = A329900(A004490(n)).

a(n) = A005940(1+A342013(n)).