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%I #36 Jan 14 2020 06:24:50
%S 1,2,3,5,7,14,52,76,2528,9536,9664,35456,138496,8456192,33665024,
%T 33673216,537444352,2148958208,137454419968
%N Numbers k such that the sum of the divisors of k (except for 1 and k) plus the sum of the digits of k is equal to k.
%C Additional terms include 537444352, 2148958208, 137454419968, 35184644718592, 9007202811510784. Are there any terms > 1 not of the form 2^k*p where p is prime and k>0? - _David A. Corneth_, Jan 08 2020
%C Terms not of the form 2^k*p do exist, for example 2^15*65713*24194197 and 2^19*1739719*2639431. - _Giovanni Resta_, Jan 08 2020
%C a(20) > 10^13. - _Giovanni Resta_, Jan 14 2020
%e The first term that is not 1 or a single-digit prime is obtained by adding the proper divisors of 14 other than 1 (2,7) to its digits (1,4): (2+7) + (1+4) = 14.
%e The second such term is 52: the proper divisors of 52 other than 1 (2,4,13,26) and its digits (5,2) sum to (2+4+13+26) + (5+2) = 52.
%t Select[Range[10^7], DivisorSigma[1, #] - # - If[# == 1, 0, 1] + Plus @@ IntegerDigits[#] == # &] (* _Amiram Eldar_, Jan 12 2020 *)
%o (PARI) is(n) = n == sigma(n)-1-if(n>1,n,0)+sumdigits(n) \\ _Rémy Sigrist_, Jan 08 2020
%Y Cf. A000203, A007953, A048050.
%Y Cf. A331093 (sum of divisors - digit sum = the number).
%K nonn,base,more,less
%O 1,2
%A _Joseph E. Marrow_, Jan 08 2020
%E a(14)-a(16) from _Rémy Sigrist_, Jan 08 2020
%E a(17)-a(19) from _Giovanni Resta_, Jan 14 2020
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