SmithNumbers

The Smith numbers $4, 22, 27, 58, 85, …$: composite integers whose digit sum equals the digit sum of their prime factors (with multiplicity).

OEISA006753↗

SmithNumbersthe composite $n$ with $\mathrm{digitSum}(n) = \sum \mathrm{digitSum}(p)$ over $n$'s prime factorisation, an infinite indexed collection.

Domain: Collections

Details

• A lazy indexed collection: $Count(SmithNumbers) = +\infty$ (McDaniel, 1987). OEIS A006753.
• $At(SmithNumbers, k)$ unranks by scanning forward, factoring each candidate -- $At(SmithNumbers, 2) = 22$ ($2+2=4$; factors $2, 11$, digit sums $2+1+1=4$).
• Membership goes through Element: $Element(4, SmithNumbers)$ is true ($4=2 \times 2$: digit sums $4 = 2+2$), $Element(6, SmithNumbers)$ is false ($6=2\times3$: digit sums $2+3=5 \ne 6$).

Enumeration

Examples

1 more kept as data, checked against the oracles

Properties #

live ↗

In$4∈\mathrm{SmithNumbers}$Out$\mathrm{True}$

live ↗

In$6∈\mathrm{SmithNumbers}$Out$\mathrm{False}$

About

Examples	3
Crosswalk	OEIS

See also: Count, At, Element, HarshadNumbers, SemiprimeNumbers