A389082 a(n) = sigma(n) * A332818(n).

1, 9, 20, 63, 42, 180, 104, 405, 325, 378, 204, 1260, 154, 936, 840, 2511, 342, 2925, 580, 2646, 2080, 1836, 888, 8100, 1519, 1386, 5000, 6552, 690, 7560, 1312, 15309, 4080, 3078, 4368, 20475, 1178, 5220, 3080, 17010, 1806, 18720, 2332, 12852, 13650, 7992, 2928, 50220, 9633, 13671, 6840, 9702, 2538, 45000, 8568

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).

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)));
A389082(n) = (sigma(n)*A332818(n));

Crossrefs

Cf. A000203, A332818, A389081, A389088.

Cf. also A341529.

Sequence in context: A377002 A344818 A341529 * A013573 A146388 A230833

Adjacent sequences: A389079 A389080 A389081 * A389083 A389084 A389085

Keyword

nonn,mult

Author

Antti Karttunen, Sep 23 2025

Status

approved