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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.
1
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
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
KEYWORD
nonn,base
AUTHOR
Ctibor O. Zizka, Feb 20 2019
STATUS
approved