A366743 - OEIS

A366743

The sum of infinitary divisors of the least coreful infinitary divisor of n.

1, 3, 4, 5, 6, 12, 8, 3, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 12, 26, 42, 4, 40, 30, 72, 32, 3, 48, 54, 48, 50, 38, 60, 56, 18, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 12, 72, 24, 80, 90, 60, 120, 62, 96, 80, 5, 84, 144, 68, 90

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OFFSET

1,2

COMMENTS

Also, the sum of unitary divisors of the least coreful infinitary divisor of n, A365296(n), since A365296(n) is a term of A138302, which is also the sequence of numbers whose sets of unitary divisors (A077610) and infinitary divisors (A077609) coincide.

The number of infinitary divisors of the least coreful infinitary divisor of n is A034444(n).

LINKS

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

FORMULA

a(n) = A034448(A365296(n)).

a(n) = A049417(A365296(n)).

a(n) = A000203(n) if and only if n is squarefree (A005117).

Multiplicative with a(p^e) = p^A006519(e) + 1.

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 - 1/(p+1) + Sum_{e>=1} 1/p^f(e)-1/p^(f(e)+1)) = 0.61865169..., where f(k) = 2*k - A006519(k) = A339597(k-1).

MATHEMATICA

f[p_, e_] := p^(2^IntegerExponent[e, 2]) + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^(2^valuation(f[i, 2], 2))); }

CROSSREFS

Cf. A000203, A005117, A006519, A034444, A034448, A049417, A077609, A077610, A138302, A339597, A365296, A366742, A366744.

Sequence in context: A103402 A154664 A371242 * A191750 A346613 A034448

Adjacent sequences: A366740 A366741 A366742 * A366744 A366745 A366746

KEYWORD

nonn,easy,mult

AUTHOR

Amiram Eldar, Oct 19 2023

STATUS

approved