This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331037 #36 Jan 14 2020 06:24:50 %S A331037 1,2,3,5,7,14,52,76,2528,9536,9664,35456,138496,8456192,33665024, %T A331037 33673216,537444352,2148958208,137454419968 %N A331037 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 A331037 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 A331037 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 A331037 a(20) > 10^13. - _Giovanni Resta_, Jan 14 2020 %e A331037 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 A331037 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 A331037 Select[Range[10^7], DivisorSigma[1, #] - # - If[# == 1, 0, 1] + Plus @@ IntegerDigits[#] == # &] (* _Amiram Eldar_, Jan 12 2020 *) %o A331037 (PARI) is(n) = n == sigma(n)-1-if(n>1,n,0)+sumdigits(n) \\ _Rémy Sigrist_, Jan 08 2020 %Y A331037 Cf. A000203, A007953, A048050. %Y A331037 Cf. A331093 (sum of divisors - digit sum = the number). %K A331037 nonn,base,more,less %O A331037 1,2 %A A331037 _Joseph E. Marrow_, Jan 08 2020 %E A331037 a(14)-a(16) from _Rémy Sigrist_, Jan 08 2020 %E A331037 a(17)-a(19) from _Giovanni Resta_, Jan 14 2020