A331099 - OEIS

%I #23 Sep 08 2022 08:46:24

%S 1,14,27,154,284,574,1264,2588,7288,49852,2342656,33550336,8589869056

%N The numbers such that the sum of their proper divisors plus the product of their digits equals the number.

%C The perfect numbers containing a 0 digit are all in this sequence.

%C a(14) > 10^13. - _Giovanni Resta_, Jan 19 2020

%e 14 is a term as A001065(14) = 10, A007954(14) = 4, and 10 + 4 = 14.

%e 2588 is a term as A001065(2588) = 1948, A007954(2588) = 640, and 1948 + 640 = 2588.

%t Select[Range[10^6], DivisorSigma[1, #] + Times @@ IntegerDigits[#] == 2 # &] (* _Amiram Eldar_, Jan 18 2020 *)

%o (Magma) [k:k in [1..2500000]| k eq &*Intseq(k)+DivisorSigma(1,k)-k]; // _Marius A. Burtea_, Jan 18 2020

%o (PARI) isok(n) = my(d=digits(n)); sigma(n) + vecprod(d) == 2*n; \\ _Jinyuan Wang_, Jan 19 2020

%Y Cf. A001065, A007954, A331098.

%K nonn,base,less,more

%O 1,2

%A _Scott R. Shannon_, Jan 09 2020

%E a(12) from _Jinyuan Wang_, Jan 19 2020

%E a(13) from _Giovanni Resta_, Jan 19 2020