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

1,1

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)

Links

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

Formula

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

Example

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

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

Prog

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

Crossrefs

Cf. A000005, A007953, A030513, A306509.

Sequence in context: A289355 A144214 A191043 * A129805 A289492 A262286

Adjacent sequences: A306507 A306508 A306509 * A306511 A306512 A306513

Keyword

nonn,base

Author

Ctibor O. Zizka, Feb 20 2019

Status

approved