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A372739
a(n) is the number of possible values of k such that the sum of aliquot coreful divisors of k (A336563) is n.
4
0, 1, 1, 0, 1, 3, 1, 0, 0, 2, 1, 1, 1, 3, 2, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 0, 0, 1, 6, 1, 0, 2, 2, 2, 1, 1, 2, 3, 0, 1, 5, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 0, 2, 1, 2, 2, 1, 2, 1, 3, 0, 0, 2, 4, 1, 0, 2, 4, 1, 0, 1, 2, 0, 0, 2, 5, 1, 1, 0, 2, 1, 1, 2, 2, 2
OFFSET
1,6
COMMENTS
A coreful divisor d of n is a divisor that is divisible by every prime that divides n (see also A307958).
LINKS
FORMULA
a(n) = 0 if and only if n is in A372740.
a(n) = 1 if and only if n is in A372742.
EXAMPLE
a(2) = 1 since there is 1 possible value of k, k = 4, such that A336563(k) = 2.
a(6) = 3 since there are 3 possible values of k, k = 8, 12 and 18, such that A336563(k) = 6.
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; seq[max_] := Module[{v = Table[0, {max}], i}, Do[i = s[k]; If[0 < i <= max, v[[i]]++], {k, 1, max^2}]; v]; seq[100]
PROG
(PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] - 1) - 1) - n; }
lista(nmax) = {my(v = vector(nmax), i); for(k = 1, nmax^2, i = s(k); if(i > 0 && i <= nmax, v[i]++)); v; }
CROSSREFS
Similar sequences: A048138, A324938, A331971, A331973.
Sequence in context: A229143 A330018 A065413 * A107131 A027200 A035654
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 12 2024
STATUS
approved