A306510 Numbers k such that twice the number of divisors of k is equal to the number of divisors of the sum of digits of k.

17, 19, 37, 53, 59, 71, 73, 107, 109, 127, 149, 163, 167, 181, 233, 239, 251, 257, 271, 293, 307, 347, 383, 419, 431, 433, 491, 499, 503, 509, 521, 523, 541, 563, 613, 617, 631, 653, 699, 701, 743, 761, 769, 787, 789, 811, 859, 877, 879, 941, 967

Offset: 1

Author

Ctibor O. Zizka, Feb 20 2019

Keywords

• nonn
• base

Comments

From Robert Israel, Jul 28 2020: (Start)

The first even term is a(2747)=68998.

Includes primes p such that A007953(p) is in A030513. (End)

Examples

			For k = 19, 2*A000005(19) = A000005(A007953(19)), 2*A000005(19) = A000005(10), thus k = 19 is a member of the sequence.
		

Links

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

Crossrefs

Cf. A000005, A007953, A030513, A306509.

Programs

Maple

filter:= proc(n) 2*numtheory:-tau(n) = numtheory:-tau(convert(convert(n,base,10),`+`)) end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 28 2020

PARI

isok(k) = (k >= 1) && (2*numdiv(k) == numdiv(sumdigits(k, 10))); \\ Daniel Suteu, Feb 20 2019

Formula

2*A000005(k) = A000005(A007953(k)).