A342012 - OEIS

%I #16 May 20 2022 05:25:49

%S 2,3,6,10,20,30,42,84,132,156,312,468,780,1020,1140,1380,2760,3480,

%T 3720,5208,7812,9324,10332,10836,21672,23688,26712,29736,49560,51240,

%U 56280,59640,61320,96360,104280,208560,219120,328680,352440,384120,453960,472680,482040,500760,510120,528840,594360,613080,641160,650520,1301040

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

%C 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.

%H Amiram Eldar, <a href="/A342012/b342012.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (PARI)

%o v073751 = readvec("b073751_to.txt");

%o A073751(n) = v073751[n];

%o A004490list(v073751) = { my(v=vector(#v073751)); v[1] = 2; for(n=2,#v,v[n] = v073751[n]*v[n-1]); (v); };

%o v004490 = A004490list(v073751);

%o A004490(n) = v004490[n];

%o 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)};

%o A319626(n) = (n / gcd(n, A064989(n)));

%o A342012(n) = A319626(A004490(n));

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

%Y Cf. also A217867, A329902.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 08 2021