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A331099
The numbers such that the sum of their proper divisors plus the product of their digits equals the number.
0
1, 14, 27, 154, 284, 574, 1264, 2588, 7288, 49852, 2342656, 33550336, 8589869056
OFFSET
1,2
COMMENTS
The perfect numbers containing a 0 digit are all in this sequence.
a(14) > 10^13. - Giovanni Resta, Jan 19 2020
EXAMPLE
14 is a term as A001065(14) = 10, A007954(14) = 4, and 10 + 4 = 14.
2588 is a term as A001065(2588) = 1948, A007954(2588) = 640, and 1948 + 640 = 2588.
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] + Times @@ IntegerDigits[#] == 2 # &] (* Amiram Eldar, Jan 18 2020 *)
PROG
(Magma) [k:k in [1..2500000]| k eq &*Intseq(k)+DivisorSigma(1, k)-k]; // Marius A. Burtea, Jan 18 2020
(PARI) isok(n) = my(d=digits(n)); sigma(n) + vecprod(d) == 2*n; \\ Jinyuan Wang, Jan 19 2020
CROSSREFS
KEYWORD
nonn,base,less,more
AUTHOR
Scott R. Shannon, Jan 09 2020
EXTENSIONS
a(12) from Jinyuan Wang, Jan 19 2020
a(13) from Giovanni Resta, Jan 19 2020
STATUS
approved