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A324535 An analog of sigma(n)-n (A001065) for nonstandard factorization based on the sieve of Eratosthenes (A083221). 4
0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 13, 14, 1, 36, 6, 16, 11, 28, 1, 42, 1, 31, 33, 20, 13, 55, 1, 22, 15, 50, 1, 66, 1, 40, 40, 26, 1, 76, 8, 43, 49, 46, 1, 54, 31, 64, 41, 32, 1, 108, 1, 34, 17, 63, 17, 144, 1, 58, 105, 74, 1, 123, 1, 40, 21, 64, 19, 78, 1, 106, 57, 44, 1, 172, 73, 46, 87, 92, 1, 201, 57, 76, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences generated by sieves

Index entries for sequences related to sigma(n)

FORMULA

a(n) = A001065(A250246(n)) = A324545(n) - A250246(n).

a(n) = A250246(n) - A324546(n).

PROG

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

A055396(n) = if(1==n, 0, primepi(A020639(n)));

v078898 = ordinal_transform(vector(up_to, n, A020639(n)));

A078898(n) = v078898[n];

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

A250246(n) = if(1==n, n, my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));

A001065(n) = (sigma(n)-n);

A324535(n) = A001065(A250246(n));

CROSSREFS

Cf. A001065, A250246, A324545, A324546.

Sequence in context: A294888 A001065 A173455 * A318501 A318325 A300244

Adjacent sequences:  A324532 A324533 A324534 * A324536 A324537 A324538

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 08 2019

STATUS

approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)