A394255 The sum of infinitary divisors of n that are numbers whose prime factorization exponents are all powers of 2 (A138302).

1, 3, 4, 5, 6, 12, 8, 7, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 28, 26, 42, 13, 40, 30, 72, 32, 19, 48, 54, 48, 50, 38, 60, 56, 42, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 39, 72, 56, 80, 90, 60, 120, 62, 96, 80, 21, 84, 144, 68, 90

Offset

1,2

Comments

The number of these divisors is A392451(n), and the largest of them is A353897(n).

Links

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

Formula

Multiplicative with a(p^e) = (1 + Sum_{k>=0} p^(2^k)), where e = Sum_{k>=0} e_k * 2^k, i.e., e_k is k-th bit of e.

Mathematica

f[p_, e_] := 1 + Total[p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], 1] // Flatten))]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n), e); prod(k = 1, #f~, e = binary(f[k, 2]); 1 + sum(i = 1, #e, if(e[i], f[k, 1]^(2^(#e-i)), 0))); }

Crossrefs

Cf. A049417, A077609, A138302, A353897, A392451.

Sequence in context: A366743 A191750 A384554 * A346613 A378433 A378434

Adjacent sequences: A394252 A394253 A394254 * A394256 A394257 A394258

Keyword

nonn,mult,easy

Author

Amiram Eldar, Mar 14 2026

Status

approved