A392062 Numbers k such that every prime factor of the sum of decimal digits of k is greater than every prime factor of k.

1, 10, 16, 25, 32, 49, 56, 98, 100, 128, 160, 175, 245, 250, 256, 289, 490, 539, 560, 595, 616, 625, 676, 728, 748, 784, 845, 847, 896, 968, 980, 1000, 1024, 1280, 1372, 1408, 1600, 1664, 1666, 1750, 1792, 1859, 1925, 1936, 1976, 2197, 2366, 2450, 2500, 2548, 2560, 2744, 2816, 2890, 2975, 3125

Offset

1,2

Comments

This includes powers of 10 (A011557), for which the condition is vacuously true as the sum of digits has no prime factors.

Otherwise, numbers k such that A020639(A007953(k)) > A006530(k).

Contains no multiples of 3.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(6) = 49 is a term because its sum of digits is 13, a prime, while the only prime factor of 49 is 7, and 13 > 7.
The first term whose digital sum is composite is a(237) = 65536 = 2^16, whose digital sum is 25.

Maple

filter:= proc(n)
  min(NumberTheory:-PrimeFactors(convert(convert(n, base, 10), `+`))) > max(NumberTheory:-PrimeFactors(n))
end proc:
select(filter, [$1..10000]);

Crossrefs

Cf. A006530, A007953, A011557, A020639.

Sequence in context: A397426 A152138 A109100 * A384602 A155151 A104788

Adjacent sequences: A392059 A392060 A392061 * A392063 A392064 A392065

Keyword

nonn,base

Author

Robert Israel, Dec 29 2025

Status

approved