A331093 -id:A331093 - cp's OEIS frontend

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.

1, 2, 3, 5, 7, 14, 52, 76, 2528, 9536, 9664, 35456, 138496, 8456192, 33665024, 33673216, 537444352, 2148958208, 137454419968

Offset: 1

Joseph E. Marrow, Jan 08 2020

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
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
a(20) > 10^13. - Giovanni Resta, Jan 14 2020

			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.
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.

Cf. A000203, A007953, A048050.

Cf. A331093 (sum of divisors - digit sum = the number).

Select[Range[10^7], DivisorSigma[1, #] - # - If[# == 1, 0, 1] + Plus @@ IntegerDigits[#] == # &] (* Amiram Eldar, Jan 12 2020 *)

is(n) = n == sigma(n)-1-if(n>1,n,0)+sumdigits(n) \\ Rémy Sigrist, Jan 08 2020

a(14)-a(16) from Rémy Sigrist, Jan 08 2020

a(17)-a(19) from Giovanni Resta, Jan 14 2020

A331096 Numbers k such that the sum of all divisors except k, minus the sum of the digits of k, is equal to k.

Original entry on oeis.org

20, 66, 138, 174, 246, 282, 318, 354, 426, 534, 606, 642, 822, 1038, 1074, 1146, 1182, 1362, 1434, 1506, 1542, 1614, 1902, 2082, 2118, 2154, 2334, 2406, 2514, 2802, 3018, 3054, 3126, 3342, 3414, 3522, 3702, 4062, 4206, 4314, 5034, 5142, 5322, 6114, 7122, 7232, 7302, 8202

Offset: 1

Joseph E. Marrow, Jan 08 2020

The first two odd elements are a(49) = 8415 and a(107) = 31815.- Robert Israel, Jan 16 2020

Robert Israel, Table of n, a(n) for n = 1..1400

Cf. A007953 (sum of digits), A001065 (sum of proper divisors).

Related sequences are A331037 and A331093.

[k:k in [1..8250]| DivisorSigma(1,k) eq 2*k+&+Intseq(k)]; // Marius A. Burtea, Jan 11 2020

filter:= proc(k) numtheory:-sigma(k)-convert(convert(k,base,10),`+`)=2*k end proc:
select(filter, [$1..10000]); # Robert Israel, Jan 16 2020

Select[Range[10^4], DivisorSigma[1, #] - Plus @@ IntegerDigits[#] == 2 # &] (* Amiram Eldar, Jan 11 2020 *)

isok(k) = sigma(k) - k - sumdigits(k) == k; \\ Michel Marcus, Jan 11 2020

cp's OEIS Frontend

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.

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