A389081 a(n) = n * sigma(A332818(n)).

1, 8, 18, 52, 40, 144, 98, 320, 279, 320, 198, 936, 156, 784, 720, 1936, 340, 2232, 570, 2080, 1764, 1584, 874, 5760, 1425, 1248, 4212, 5096, 696, 5760, 1302, 11648, 3564, 2720, 3920, 14508, 1184, 4560, 2808, 12800, 1804, 14112, 2322, 10296, 11160, 6992, 2914, 34848, 8967, 11400, 6120, 8112, 2544, 33696, 7920

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..26921

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

a(n) = n * A389073(n).

Prog

(PARI)
up_to = 26921;
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
A108546list(up_to) = { my(v=vector(up_to), p, q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4, up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
v108546 = A108546list(up_to);
A108546(n) = v108546[n];
A108548(n) = { my(f=factor(n)); f[, 1] = apply(A108546, apply(primepi, f[, 1])); factorback(f); };
A332806list(up_to) = { my(v=vector(2), xs=Map(), lista=List([]), p, q, u); v[2] = 3; v[1] = 5; mapput(xs, 1, 1); mapput(xs, 2, 2); mapput(xs, 3, 3);  for(n=4, up_to, p = v[2-(n%2)]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[2-(n%2)] = q; mapput(xs, primepi(q), n)); for(i=1, oo, if(!mapisdefined(xs, i, &u), return(Vec(lista)), listput(lista, prime(u)))); };
v332806 = A332806list(up_to);
A332806(n) = v332806[n];
A332808(n) = { my(f=factor(n)); f[, 1] = apply(A332806, apply(primepi, f[, 1])); factorback(f); };
A332818(n) = A108548(A003961(A332808(n)));
A389081(n) = (n*sigma(A332818(n)));

Crossrefs

Cf. A332818, A389073, A389082, A389088.

Cf. also A341528.

Sequence in context: A066721 A079704 A341528 * A032795 A120543 A337836

Adjacent sequences: A389078 A389079 A389080 * A389082 A389083 A389084

Keyword

nonn

Author

Antti Karttunen, Sep 23 2025

Status

approved