A392437 - OEIS

A392437

3-composable numbers: numbers k divisible by 3 but not by 2, for which k/3 is a sum of the other nontrivial divisors of k.

135, 225, 315, 345, 405, 495, 525, 585, 675, 765, 855, 945, 975, 1035, 1125, 1155, 1197, 1215, 1305, 1365, 1395, 1425, 1485, 1575, 1617, 1665, 1725, 1755, 1785, 1845, 1935, 1953, 1995, 2025, 2079, 2115, 2145, 2205, 2295, 2331, 2385, 2415, 2457, 2475, 2565, 2583

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

An integer n > 1 is a term if and only if 3 is the smallest prime divisor of n, and its largest proper divisor L = n/3 can be represented as the sum of some subset of its other nontrivial divisors. A 'nontrivial divisor' d of n is any divisor that is 1 < d < n. Let D_{3}(n) = {1 < d < L : d | n}. Then n is a term if there exists a subset S of D_{3}(n) such that L = Sum(S). Written in this form, n is recognizable as a p-composable number with p = 3, where the case for general p is defined in A392440.

LINKS

Table of n, a(n) for n=1..46.

Peter Luschny, Composable, rigid, and sparse numbers. A Python notebook.

PROG

(Python) # Function 'is_composable' is defined in A392440 (see also links).

def A392437_list(upto: int) -> list[int]:

return [n for n in range(135, upto+1, 3) if 3 == is_composable(n)]

print(A392437_list(2584))

CROSSREFS

Cf. A392440, A392438 (p=2), A392500

Sequence in context: A359597 A218417 A348696 * A274434 A325569 A372567

Adjacent sequences: A392434 A392435 A392436 * A392438 A392439 A392440