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 A240894 Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n) - n = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)}) - Sum_{j=1..i}{d_(j)*10^(j-1)}} (see example below). 17
 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 131, 211, 241, 271, 311, 331, 431, 461, 541, 571, 631, 641, 661, 761, 811, 899, 911, 941, 971, 1601, 3701, 5101, 5701, 6101, 6701, 8101, 9601, 13001, 19001, 24001, 54001, 69001, 93001, 97001, 102737, 194357, 217267 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Mainly primes. The first composite numbers in the sequence are 899, 102737, 194357, 217267, 377149, etc. LINKS Giovanni Resta, Table of n, a(n) for n = 1..135 (terms < 10^10) EXAMPLE If n = 194357, starting from the least significant digit, let us cut the number into the set 7, 57, 357, 4357, 94357. We have: sigma(7) - 7 = 1; sigma(57) - 57 = 23; sigma(357) - 357 = 219; sigma(4357) - 4357 = 1; sigma(94357) - 94357 = 759 and 1 + 23 + 219 + 1 + 759 = 1003 = sigma(194357) - 194357. MAPLE with(numtheory); P:=proc(q) local a, k, n; for n from 2 to q do a:=0; k:=1; while (n mod 10^k)

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Last modified December 6 22:25 EST 2021. Contains 349567 sequences. (Running on oeis4.)